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Step 1
Heat the oven to 425°F. In a large roasting pan, rub the tomato paste over the beef bones and beef shanks. Add the onions, garlic, carrots and celery to the pan. Put the pan in the oven and roast for 30 minutes. Turn the beef and aromatics and roast for another 15 to 30 minutes, until the beef and aromatics are browned. Scrape everything from the roasting pan into the pressure cooker pot. Add the thyme and peppercorns to the pot and cover the bones with water – 8 to 12 cups of water, or whatever reaches your pot’s max fill line. Lock the lid on the pressure cooker and pressure cook on high for 75 minutes in an electric PC, 1 hour in a stovetop PC. Let the pressure come down naturally, about 30 more minutes. (The water holds a lot of heat, so it takes a while for the pressure to drop. If you get impatient, you can quick release the heat after 15 minutes.) Scoop the solids out of the pot with a slotted spoon, then pour the broth through a fine mesh strainer. Skim the fat from the top of the broth as best you can. (This is easy if you refrigerate the broth overnight; the fat rises to the top and solidifies, so you can scrape it off in big chunks). Use 2 quarts of the broth in this recipe, and freeze the rest of the broth in 2 cup containers for later use.
Step 2
Wipe out the pressure cooker pot, then put it back over medium heat (sauté mode) and heat 1 tablespoon vegetable oil until it shimmers, about 3 minutes. Brown the beef cubes on one side, working in in two batches so we don’t crowd the pot. Brown the first batch of beef cubes on one side, about 4 minutes, then transfer to a bowl. Add the second batch, brown it on one side (again, about 4 minutes), then move it to the bowl with the rest of the beef.
Step 3
Add the onion and garlic to the pot, and sprinkle with 1/2 teaspoon of salt and the dried thyme. Sauté until the onion turns translucent, about 5 minutes, occasionally scraping the bottom of the pot with a flat-edged wooden spoon to work loose the browned bits of beef.
Step 4
Add browned beef and any juices in the bowl, the beef broth, the crushed tomatoes, and the potatoes. Stir to mix everything up in the pot. Lock the pressure cooker lid. Pressure cook on high pressure (manual mode) for 15 minutes in an electric PC or 12 minutes in a stovetop PC, and then quick release the pressure. (Or, if you have the time, pressure cook for 12 minutes in an electric PC, 10 minutes in a stovetop PC, and let the pressure come down naturally, about 20 more minutes.)
Step 5
Set the pressure cooker to sauté mode adjusted to high (or turn on medium-high heat) and pour in the frozen mixed vegetables. Let the frozen vegetables heat through, about 5 minutes.
Step 6
There is very little salt in this homemade broth, so you will need to season the soup heavily. Add salt until the taste picks up – it goes from flat and boring to sweet and delicious. (I added 1 1/2 teaspoons of fine sea salt to get the broth tasting the way I wanted it to.) Also stir in fresh ground black pepper; I like about 1/2 teaspoon for 8 cups of broth. Serve and enjoy!