Preheat oven to 375º. In a large pot of boiling water, cook elbows according to package directions until al dente. Drain and return to pot.
Meanwhile, in a large skillet over medium heat, melt butter. Add shallot and garlic and cook until fragrant and softened, 3 minutes. Add flour and whisk until combined and golden, 1 minute. Add milk and season with salt and pepper. Simmer 2 minutes, until sauce is thickened and smooth.
Stir in ½ white cheddar and mozzarella until melty, then remove from heat.
Add sauce and crab meat to pot with cooked elbows and stir until completely combined.
Sprinkle with remaining ½ cup cheddar and parsley and bake until bubbly, 20 minutes.
