Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish with 1 teaspoon butter.
Bring a large pot of lightly salted water to a boil. Cook elbow macaroni in the boiling water, stirring occasionally, until tender yet firm to the bite, about 8 minutes.
Melt 3 tablespoons butter in a saucepan over medium heat while macaroni is cooking. Add flour and whisk until fragrant, 2 to 3 minutes. Pour in a little milk and continue whisking. Pour in remaining milk and add frozen spinach. Cook, whisking constantly, until spinach softens and sauce thickens, about 5 minutes.
Remove sauce from heat and stir in 2 cups Cheddar cheese; whisk until melted. Season sauce with salt, pepper, and nutmeg.
Drain macaroni and spread evenly in the prepared baking dish. Cover with cheese sauce. Mix well. Sprinkle remaining 1 cup Cheddar cheese on top.
Bake in the preheated oven until cheese is melted, about 30 minutes. Turn on the oven's broiler and broil until a golden crust forms on top, about 3 minutes.