For the pumpkin, just use canned pumpkin puree (not pumpkin pie mix). In North America, this is probably Libby's or E.D. Smith brand, available in most supermarkets year-round usually in the baking aisle. I've scaled this recipe to use exactly 1 29-ounce can of pureed pumpkin, but a little more or less won't hurt. (Pureed pumpkin lasts forever in the freezer; just put it in a ziplock bag and flatten it out.)
You can roast your own pumpkins if you want, but I've tried it in both pies and beer and couldn't tell the difference, and it's more work to get basically the same product. Quarter the pumpkin and remove the seeds. Steam for 30 minutes, or roast at 425°F/215°C until soft, probably at least 1 hour but depends on the size and thickness of your pumpkin. Scrape the flesh away and puree in a food processor. Don't use a jack-o'-lantern pumpkin for this, as they're bred for size and not flavor; instead use Sugar Pie or similar small varieties of pumpkin. Canned pumpkin is sometimes partly or entirely squash, not necessarily pumpkin; feel free to substitute other hard winter squash like Hubbard, kabocha, or acorn squash. You could even try using sweet potatoes.
The pumpkin will leave a lot of trub in the mash and boil. After the boil, use a filter if you have one. If not, definitely rack the wort into the carboy rather than pouring or draining it. Before racking, stir the wort in the kettle very hard to get a strong vortex going, and then let it settle for at least 10-20 minutes. The heavy trub should be forced to the middle, and you can rack from the outside edge to avoid sucking too much of it up.
For the vanilla extract, you definitely want to make your own; buying 4 ounces would make this a ridiculously expensive brew. Moreover, you might as well add the pumpkin pie spice (and you should mix your own from whole cinnamon, nutmeg, ginger, allspice, and cloves) to extract it, too. Cut and scrape 2 vanilla beans, and put all of it (including the pods) into a small jar. Optionally add the pumpkin pie spice (or whole spices). Add 4 ounces vodka. Let this sit for at least 2 weeks, shaking occasionally.
The graham cracker extract is essential; it gives it that "pumpkin pie" flavor that I feel makes Southern Tier's taste so much better than other pumpkin beers. The amount to add is 1 teaspoon (5 milliliters); I measured this and it seems to be 4 grams. Add it in secondary if you're bottline, otherwise add it at kegging so as not to leave any behind in the carboy, which you could also do with the vanilla and spice extract.
The water adjuncts are obviously specific to my local water.
Clone of Southern Tier's Pumpking (https://stbcbeer.com/beers/pumking-imperial-ale/).
Based on https://www.brewersfriend.com/homebrew/recipe/view/16367/southern-tier-pumking-clone, but modified enough that I really only claim their recipe as a second inspiration.
