Preheat your oven to 275°F and line a large baking sheet with foil. I always do this first because forgotten preheating is a recipe disaster I've made twice before.
Pat the beef ribs completely dry with paper towels, then place them on the prepared sheet. Moisture on the surface prevents browning, so this step matters more than most people realize.
Combine brown sugar, garlic powder, onion powder, paprika, cumin, black pepper, and salt in a small bowl. Mix until the spices are evenly distributed, which takes about 30 seconds of stirring.
Brush olive oil across both sides of the ribs, then massage the spice mixture into every crevice and side. This is your moment to get hands-on because the rub won't penetrate with careless application.
Let the seasoned ribs sit at room temperature for 15 minutes — I confess I skipped this once and the flavor was noticeably flatter. The spices begin activating and blooming during this rest, creating a deeper foundation for roasting.
Spread tomato paste thinly over the top of the ribs, then slide the sheet into the 275°F oven. Cover loosely with foil so steam circulates while the ribs cook covered for the first 90 minutes.
Remove foil and continue roasting for another 90 minutes uncovered, checking at the 150-minute mark to ensure they're not drying out. The meat should pull from the bone with minimal resistance by this point — that's your signal you're nearly done.
Test doneness by piercing between the bones with a fork; if it slides through like butter, your fall off bone beef ribs family dinner is ready. Remove from the oven and let rest for 5 minutes before serving so the juices redistribute.