Butter the muffin cut sides with 2 tablespoons butter. Toast cut-side down in a skillet over medium heat for 2-3 minutes; set aside.

Cook the four sausage patties according to package directions until the centers reach 160°F; keep warm.

Melt remaining tablespoon butter over medium-low heat. Add eggs and cook, turning carefully, until whites and yolks are firm, about 3-4 minutes per side. Top each with cheese during the last minute.

Fill each muffin with sausage and a cheesy egg; serve.

For freezing, refrigerate sandwiches promptly until cold, then wrap individually and freeze. Remove ALL foil before microwaving. Place on a microwave-safe plate, cover with a paper towel, and heat in short intervals, turning as needed, until the center reaches 165°F. Timing depends on microwave power and sandwich size.