Preheat a skillet over medium heat and add 1 tablespoon olive oil.
Cook the turkey sausage patties in the skillet for about 4-5 minutes per side until fully cooked and browned. Remove from skillet and set aside.
In a medium bowl, whisk together the eggs, whole milk, salt, and black pepper until well combined.
In the same skillet, melt 2 teaspoons of unsalted butter over medium-low heat.
Pour the egg mixture into the skillet and cook gently, stirring occasionally with a spatula, until the eggs are softly scrambled and cooked through, about 3-4 minutes. Remove from heat.
Slice the ciabatta rolls horizontally and toast them lightly in the oven or on a dry skillet until golden and crisp.
Place 2 slices of cheddar cheese on the bottom half of each toasted ciabatta roll.
Divide the scrambled eggs evenly over the cheese slices, then top each with a cooked turkey sausage patty.
Add fresh spinach leaves on top of the sausage patties.
Cover with the top halves of the ciabatta rolls to complete the sandwiches.
Serve immediately while warm.