Heat the oil in a
12-inch nonstick skillet over medium-high.
Add garlic and cook, stirring, for 30 seconds.
Add shrimp. Sprinkle with the smoked paprika, salt, and pepper. Cook, moving frequently around the pan (or flipping once if they're large and fit in a single layer), until just opaque in the center — a couple minutes total, depending on size.
Add spinach and cook until just wilted. Drain and discard any liquid.
Arrange four of the tortillas on a work surface. Using about ⅔ of the cheese, sprinkle each tortilla evenly, leaving a slight border around the edge to account for melting. Top each tortilla evenly with beans and the shrimp and spinach mixture. Sprinkle with remaining cheese, then top each with one of the four remaining tortillas.
Wipe the pan clean and place over medium heat. One at a time, cook quesadillas until tortillas are browned in spots and cheese is fully melted, flipping once. (See note 6 below for oven instructions if you prefer.)
To serve, cut into wedges. Stir a tablespoon of milk or water into the sour cream and drizzle over quesadillas. Sprinkle with pickled onions if using.