Step 1

Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Heat oil; add carrot, onion, celery, and garlic. Cook, stirring occasionally, until onions are translucent, about 5 minutes. Turn off Saute mode.

Step 2

Stir chicken broth, beans, paprika, and thyme into the pot. Close and lock the lid; move the valve to Sealing. Select high pressure according to manufacturer's instructions; set timer for 34 minutes. Allow 10 to 15 minutes for pressure to build.

Step 3

Select Cancel/Keep Warm when cooking is done. Release pressure for 10 minutes using the natural-release method according to manufacturer's instructions. Move valve carefully to Venting and release remaining pressure using the quick-release method, about 5 minutes.

Step 4

Unlock and remove lid; stir ham and tomatoes into the bean mixture. Close and lock the lid; move the valve to Sealing. Select high pressure according to manufacturer's instructions; set timer for 7 minutes. Allow 10 to 15 minutes for pressure to build. Release pressure carefully using the quick-release method, about 5 minutes. Season soup with salt and pepper.