Step 1

Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain.

Step 2

Preheat oven to 350 degrees F (175 degrees C).

Step 3

Grease a 1 1/2-quart baking dish.

Step 4

Melt 3 tablespoons butter in a skillet over medium heat. Stir in the ham and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes.

Step 5

Stir potatoes into ham mixture; transfer to the prepared baking dish.

Step 6

Melt 1/4 cup butter in a saucepan over medium heat. Stir flour into melted butter until smooth.

Step 7

Gradually whisk milk into flour mixture; season with salt and black pepper. Continue cooking and stirring until thickened, about 2 minutes.

Step 8

Reduce heat to medium-low and stir Cheddar cheese into the white sauce until melted.

Step 9

Pour sauce over ham and potatoes.

Step 10

Sprinkle bread crumbs atop casserole.

Step 11

Bake in the preheated oven until sauce is bubbly and browned, 25 to 30 minutes.