Place a 12-inch skillet over medium-low heat and add the olive oil. Swirl to coat the bottom evenly, then scatter the diced potatoes into the pan in a single, even layer. Let them cook undisturbed for 4 to 5 minutes until they release easily from the surface. Stir and continue cooking for another 3 to 4 minutes until the edges are golden and the centers are nearly fork-tender.

Add the minced garlic and cook briefly, about 1 minute, until its aroma becomes fragrant but not browned. Deglaze the pan with the dry white wine, scraping up any flavorful bits stuck to the base.

Stir in the navy beans, followed by the smoked paprika, garlic powder, onion powder, and crushed red pepper flakes. Toss gently until the spices are well-distributed and coat the potatoes and beans uniformly.

Pour in the crushed tomatoes and bring the mixture to a gentle boil. Lower the heat to a simmer and allow the sauce to cook for 6 to 8 minutes, or until it thickens slightly and the potatoes are fully tender. If a looser consistency is desired, gradually stir in the vegetable broth to reach your preferred texture.

To finish, drizzle in the remaining tablespoon of olive oil, fold in the vegetarian parmesan, and season with salt to taste. Serve warm by spooning the spicy bean and potato mixture generously over bowls of cooked brown rice.