Preheat oven to 400 degrees F.
Brush a baking dish or pie pan with 2 tablespoons melted butter.
Line the bottom of your baking dish or pie pan with the bread slices, trimming as necessary to fit, so that they cover the entire bottom of the dish in a single layer.
Top bread layer with shredded hashbrowns (you may not use the whole bag). Top with remaining 2 tablespoons melted butter.
Place in oven and allow to begin to bake while oven is still preheating.
Meanwhile, heat olive oil in a skillet over medium-high heat, and cook bacon briefly, about 3 minutes. Add onion, thyme, garlic, salt, and pepper. Reduce heat to medium and cook until softened, stirring frequently, about 12 minutes.
In a large bowl, whisk together eggs, half and half, nutmeg, and Dijon mustard until smooth. Add the bacon mixture and stir to combine.
Pour the filling over the semi-baked crust. Return to oven and bake for 15 minutes.
Top evenly with summer sausage and gruyère cheese.
Continue baking until browned and bubbling, about 15 more minutes. Serve warm with a garnish of fresh thyme.