Mash Some Of The Beans. For thicker texture, mash one can of the drained, rinsed beans slightly to break up some of the beans. Add the beans to a small bowl and use a potato masher or the bottom of a sturdy cup to mash the beans. You don't need to mash them completely to puree, just mash them to break them up. Set aside while you cook the chicken.
Cook Chicken. Heat the olive oil in the Instant Pot on SAUTE mode. Add the ground chicken and cook 5-7 minutes, or until chicken is completely cooked through.
Add Veggies. Next, add the onion, carrots, and celery to the Instant Pot and cook 3-4 minutes to soften slightly.
Build Flavor. Add tomato paste, 1/4 cup Frank's hot sauce, chili powder, cumin, salt, and dried dill (if using). Cook just 1-2 minutes, stirring well to combine.
Add Broth & Beans. Pour in 2 cups of chicken broth and stir to scrape up any stuck on bits from the bottom of the pan. Then, add the can of full beans, and the mashed beans. Stir to combine.
Cook Chili. Press CANCEL to end the SAUTE mode. Secure the lid, making sure that the steam valve is set to SEALING not VENTING. Cook the chili on HIGH PRESSURE (Manual) for 8 minutes. Note that it will take about 10 minutes for the Instant Pot to come up to pressure.
Naturally Release Steam for 10 minutes, then use an oven mitt or spoon to carefully quick release the rest of the pressure by switching the pressure valve to the VENTING position.
Season & Thicken, If Desired. Taste the chili and add additional salt, seasonings, or hot sauce, to taste. Stir in 1 Tablespoon butter (optional), then the fresh cilantro. If you want even thicker chili, you can mix 1 Tablespoon cornstarch with 1 Tablespoon cold water and stir it into the chili. Cook 2-3 minutes on LOW, until the chili has thickened. (Keep in mind, the chili will continue to thicken, as it cools.)
Serve & Store. Enjoy warm with your favorite chili toppings. Store leftover chili in an airtight container in the refrigerator 3-4 days, or freeze up to 2 months. Thaw frozen chili in the refrigerator, then re-heat in the microwave or on the stovetop for best results.