Preheat oven to 375℉. Preheat a skillet to medium heat. Add 2 tablespoons of the butter. Constantly whisk until the butter is brown and becomes nutty and fragrant. This can take 7-8 minutes or so. Watch carefully..it can burn quick!
Once butter is brown, add the sage leaves and cook for 30 seconds to 1 minute, until golden and crispy. Remove leaves from pan and set on paper towels to drain. Add the breadcrumbs to the brown butter and toss to combine. Reserve until ready to bake.
In a medium saucepan over medium heat, add the remaining 2 tablespoons of butter. Once melted, add the flour and whisk to combine. Cook for 1-2 minutes, whisking constantly until slightly golden. Slowly pour in the milk, whisking constantly to combine. Raise heat to high. Continue to whisk until mixture comes to a boil and thickens.
Add the cheeses gradually, stirring until smooth. Add the nutmeg, dijon, salt, and pepper. Season to taste with additional salt, pepper, or nutmeg if desired. Add the gnocchi and stir to coat. Add to a baking dish and top with breadcrumbs. Bake for 20 minutes or until bubbly and golden. Add the sage leaves on top and serve!