Cook the sausage: In a medium skillet over medium-high heat, cook the breakfast sausage, breaking it apart with a spatula, until browned and cooked through, about 6–8 minutes. Drain any excess grease and transfer the cooked sausage to a plate. Wipe out the skillet if needed before cooking the eggs.
Scramble the eggs: In a bowl, beat the eggs with a pinch of salt and pepper. Melt 1 tablespoon of butter in the same skillet over medium heat. Pour in the eggs and cook gently, stirring occasionally, until soft curds form and the eggs are just set — about 2–3 minutes. Be careful not to overcook; they should remain slightly creamy. Remove from heat and set aside.
Assemble the sandwiches: Lay out the sourdough slices on a clean surface. Spread a light layer of softened butter on one side of each slice (this will be the outer side that touches the pan). On the unbuttered side of half the slices, layer one slice of cheese, a portion of scrambled eggs, some cooked sausage, and another slice of cheese. Top each with a second slice of bread, buttered side facing out.
Grill the sandwiches: Heat a large skillet or griddle over medium-low heat. Place the sandwiches in the pan and cook for 3–4 minutes per side, pressing gently with a spatula, until the bread is golden brown and crisp and the cheese inside is fully melted. Work in batches if necessary to avoid crowding the pan.
Serve and enjoy: Slice the grilled sandwiches diagonally and serve warm. For extra flavor, sprinkle with chopped chives or serve with a drizzle of hot sauce or ketchup on the side. The combination of buttery bread, savory sausage, creamy eggs, and melted cheese makes every bite irresistible.
Optional variations: Add sliced tomato, cooked bacon, or a handful of spinach before grilling for extra flavor and texture. For a richer version, use brioche bread instead of sourdough.