Preheat a skillet over medium heat and add the olive oil.
Cook the turkey sausage patties in the skillet for 4-5 minutes on each 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.
Add the butter to the same skillet and melt over medium-low heat.
Pour the egg mixture into the skillet and cook gently, stirring frequently with a spatula, until the eggs are softly scrambled and just set, about 3-4 minutes. Remove from heat.
Slice the ciabatta rolls horizontally and toast them lightly in the skillet or toaster until golden brown.
Place two slices of cheddar cheese on the bottom half of each toasted ciabatta roll.
Divide the scrambled eggs evenly over the cheese slices.
Top the eggs with two turkey sausage patties per sandwich.
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.