Rub paprika, salt, and pepper all over pork. Spray a large skillet with cooking spray and heat over medium-high. Add pork and sear all sides; approximately 10 minutes. Place into large crock pot.
Add broth, balsamic vinegar, molasses, and soy sauce to the hot skillet. Bring to a boil while scraping pan to remove the cooked-on brown bits. Pour over pork in crock pot. Slice onion and garlic; add to pork. Cook on low for 6 1/2 hours.
Remove pork and place onto cutting board, reserving liquid. Shred pork and set aside, along with the cooked onions.
Skim fat from reserved liquid and discard. Add liquid to skillet and add cider vinegar; bring to a boil and cook for 10 minutes. (Here is a great tip from Cooking Light: After crock pot liquid has cooled to touch, add to a ziplock bag. Seal it and allow to stand and rest for 10 minutes while the fat rises to the top. While holding upright bag over a skillet, carefully snip off a bottom corner and allow liquid to drain just before the fat layer reaches the bottom. Discard the fat.)
At this point cook the egg noodles as directed on package and set aside.
Whisk together the water and corn starch. Gradually add to boiling drippings in skillet; allow to thicken, stirring constantly. Add pork and onions, and stir until combined.
Place beans in a microwave-safe dish along with a small amount of liquid. Cover and cook for 5 minutes until hot and slightly softened (adjust cooking time according to desired tenderness).
Serve pork over noodles with beans and mango on the side.