Cook onion in oil in a skillet over medium heat for 6 minutes. Stir in garlic and paprika for 30 seconds; immediately add broth and tomato paste.
Pour into a 6-quart slow cooker. Stir in pork, peppers, salt, and pepper.
Cover; cook on low about 6 hours until pork is fork-tender and reaches at least 145°F. Mix cornstarch with cold water; stir into sauce. Cover; cook on high 10 minutes.
Boil noodles according to package directions until just tender, about 8 to 10 minutes; drain.
Turn off cooker; let bubbling stop for 5 minutes. Gradually whisk 1/2 cup hot sauce into yogurt; stir into cooker without boiling again.
Divide noodles, pork, and pepper sauce among 6 bowls.