Gnocchi Gratin with Ham and Peas

1 package 16 oz. potato gnocchi
6 tablespoons unsalted butter, divided
1 pound ham steak, cut into 1/2-inch pieces
1/4 cup all-purpose flour
2 cups whole milk
1/4 teaspoon kosher salt
1/4 teaspoon black pepper
1/2 cup shredded Gruyère cheese
1/2 cup grated Parmesan cheese, divided
1 cup thawed frozen green peas

Preheat oven to 400°F.
Cook potato gnocchi according to package directions; drain and transfer to a large bowl.
Melt 2 Tbsp. unsalted butter in a large Dutch oven over medium-high.
Add ham and cook, stirring often, until ham is lightly browned and any moisture has evaporated, 5 to 6 minutes.
Using a slotted spoon, transfer ham to bowl with gnocchi.
Melt 4 Tbsp. unsalted butter in Dutch oven over medium-high.
Whisk in all-purpose flour. Cook, whisking constantly, until mixture is light golden brown, 1 to 2 minutes.
Slowly whisk in whole milk, and bring to a boil; whisk vigorously to work out any lumps.
Whisk in kosher salt and black pepper.
Remove from heat, and slowly whisk in shredded Gruyère cheese and 1/4 cup grated Parmesan cheese, until melted.
Pour cheese sauce over ham and gnocchi; stir in thawed frozen green peas.
Transfer mixture to a lightly greased 11-x 7-inch baking dish.
Sprinkle remaining 1/4 cup grated Parmesan cheese on top, and bake in preheated oven until bubbly and golden brown, 20 to 25 minutes.
Remove from oven, and serve warm.