Lightly crush saffron with fingers; steep in 1/4 cup hot broth 10 minutes. Keep remaining broth warm.
Heat oil in a deep 12-inch skillet over medium-high. Brown beef and onion 8 to 10 minutes, crumbling beef, until 160°F. Drain excess fat if needed.
Stir garlic and smoked paprika 30 seconds; add rice and stir 1 minute.
Add tomato puree, all broth including saffron infusion, peppers, olives, black pepper, and salt. Simmer; spread rice evenly.
Cover tightly; cook on low 22 to 25 minutes until rice is tender and liquid absorbed. If rice is firm and skillet dry, add 2 tablespoons water; cover and cook 3 minutes more.
Remove from heat; rest covered 8 minutes. Gently fold from edges to loosen rice; divide among four bowls.