If you intend to preserve the stew by canning, then you should begin by preparing canning jars according to the manufacturers directions for processing in a pressure canner. This usually involves washing jars, lids and rings in hot water, then set them aside in a protected location where they are likely to remain clean.
Preparing the vegetables: If you haven't already done so, you should prepare the raw vegetables before handling the meat, or doing any cooking. Potatoes and carrots should be thoroughly cleaned and, if desired, peeled; then cut into chunks no larger than 1" in any dimension. To a point, smaller is better: ideally, the chunks should be cubes, about ⁵⁄₁₆" to ¾" on the edges. Celery stalks should be cut into pieces about 1" long, and split lengthwise into sticks about ¼" thick; the green onions should be chopped into pieces about ¾" long; and the dry, outer layers of the pearl onions should be peeled off, leaving the remaining onion whole.
Preparing the meat: I prefer to use a large round roast, since I can get it for a lower per-pound cost than regular, butcher-cut stew meat; also, when I do that, I know exactly what I'm getting. If you buy your meat the way I do, you have some work to do before you can actually start cooking, so remove any excessive fat from the meat, and cut into cubes ½" to 1" on the edge.
Your cooking oil can be pretty much any kind of edible cooking oil, including butter, lard, bacon drippings, etc... but I prefer, and habitually use, extra-virgin olive oil. If smoking oil bothers you, I recommend peanut or corn oil. Whatever oil you use, heat it to frying temperature in a large skillet or sauce pan, and sear the meat cubes on all sides. If your pan isn't large enough to do the whole job at once, you might have to brown the meat in smaller batches. If you notice a significant amount of water cooking out of the meat, you'll need to cook off the excess water between batches. As the meat becomes ready, remove it to the large stock pot.
Cook off any water remaining in the skillet, after searing the beef, then deglaze the skillet with the red wine, reducing the volume by about half. Add the brown sugar, Worcestershire sauce, black pepper, and allspice, blending with a wire whisk. If you are not planning to can the stew, and want a thicker gravy you can incorporate about ¼ cup of flour, again using the wire whisk, but do not add thickeners to products which are intended to be canned! When all components are fully incorporated and smoothly blended, remove the pan from heat and add the contents of the pan to the stock pot.
Add the beef stock, along with the prepared vegetables, salt, thyme, and garlic, to the stock pot. Additional hot broth, or water, up to 1 quart, may be needed to compensate for liquid loss due to evaporation. Heat the stew to boiling, on medium-high heat.
If you are preparing this recipé for canning, rather than immediate consumption, then skip this step. Once the stew has achieved a boil, add your preferred thickener, if desired, and reduce the heat to a simmer. Let the stew simmer for about 1½ hours after achieving a boil, and serve! Store any leftovers in the refrigerator. Stop here! You are done!
If you intend to preserve the stew by canning, then again, do not add any thickener! Current policy in food-safety circles is that thickeners in general increase the likelihood of botulism in even pressure-canned foods, especially low-acid canned foods!
After having brought the stew back to a boil, use a slotted spoon to apportion hot stew solids equally among the eight, quart sized, canning jars, while trying to insure that there is at least one pearl onion in each jar. At least initially, do not fill any individual jar much more than ¾ full with solids. Continue stirring meanwhile, in order to insure good distribution of all of the stew's components.
When all of the solids have been transferred, fill each jar with hot stew broth, leaving 1" head space, and be sure to release any trapped air bubbles. You should add more hot broth (if you have it) or boiling water, if necessary, to achieve the desired liquid level in each jar.
Apply canning lids and rings, according to the manufacturer's instructions, and process according to your canner's instructions. I use an All-American® pressure canner that can process 4 quart jars at one time, and for this stew, at my altitude, it requires me to process them at 15 psi for 90 minutes.
To use the canned product, simply decant a jar of the stew into a sauce pan and heat to boiling; add any desired thickener, then simmer for about 10 minutes and serve. A nice roux makes a good thickener.