Preheat oven to 425 degrees F. In a bowl, combine cheeses with panko bread crumbs, then set aside.
In a large skillet, heat 1 tablespoon olive oil over medium-2 heat. Add shallot with a sprinkle of salt and cook until soft, about 5 minutes. Add in 2 of the minced garlic cloves and cook for 30 seconds, then add in white beans and stir. Let beans heat for 3-4 minutes, then remove 2 cups of beans and place them in a blender. Add in stock, milk, 1 tablespoon olive oil, salt and pepper, blending until totally smooth. Pour contents back into the skillet and stir to combine.
Spray a baking dish [mine was 6×10, but any dish you want is fine – round, square, etc] with nonstick spray. Scoop bean mixture into the dish and spread with a spatula to even out the top. Lay cheese and bread crumb mixture over top. Drizzle with remaining olive oil. Bake for 23-25 minutes, until top is golden and bubbly. Serve immediately.