Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add polenta and cook in a single layer, stirring occasionally, until beginning to brown, 8 to 10 minutes. Transfer to a plate.
Reduce the heat to medium, add the remaining 2 teaspoons oil and garlic to the pan, and cook, stirring, until fragrant, 30 seconds. Add onion and bell pepper; cook, stirring, until just tender, 3 to 5 minutes. Sprinkle with paprika; cook, stirring, for 30 seconds. Stir in beans, spinach and broth; cook, stirring, until the beans are heated through and the spinach is wilted, 2 to 3 minutes. Remove from the heat; stir in cheese and vinegar. Serve vegetables over polenta. Sprinkle with paprika, if desired.