In a large skillet over medium-high heat, heat 2 Tbsp. oil. Add 2 slices of bread and cook, turning halfway through, until golden brown on both sides, 3 to 4 minutes total. Transfer to a plate. Repeat with remaining bread and 2 Tbsp. oil. Wipe out skillet.
In same skillet over medium heat, melt butter. Add ½ tsp. pepper and cook, stirring frequently, until fragrant, 30 to 60 seconds.
Add Parmesan, Pecorino, salt, 1 can of beans, and ½ c. water. Bring to a simmer over medium-high heat; reduce heat to medium-low and continue to simmer, stirring occasionally, until slightly thickened, 2 to 3 minutes.
Fold in ½ tsp. pepper and remaining 1 can of beans; season with salt, if needed.
Divide bean mixture among bowls. Top with Parmesan; season with pepper.
