Cook Sausage: Heat olive oil in a large skillet over medium heat. Add sausage and cook, breaking it up, until browned and cooked through (5-7 minutes). Set aside.
Make Filling: In a large bowl, whisk eggs and Greek yogurt until smooth. Stir in basil, thyme, black pepper, salt, and red pepper flakes. Add cooked sausage and squeezed dry spinach. Mix until combined.
Prepare Olives & Tomatoes: In a small bowl, combine sliced olives and chopped sun dried tomatoes. Set aside.
Preheat & Prep Phyllo: Preheat oven to 350°F (177°C). Unroll phyllo sheets and cover stack with a damp paper towel to prevent drying.
First Phyllo Layer: Place 1 phyllo sheet in a 9x13 baking dish. Brush lightly with oil. Repeat with 8 more sheets, brushing each with oil (9 sheets total).
First Filling Layer: Sprinkle half the cheddar cheese over the phyllo. Dollop half the spinach sausage mixture over the cheddar. Top with half the Havarti cheese and half the olive tomato mixture.
Second Phyllo Layer: Layer 9 more phyllo sheets on top, brushing each with oil.
Second Filling Layer: Sprinkle remaining cheddar over phyllo. Add remaining spinach sausage mixture, then remaining Havarti and olive tomato mixture.
Third Phyllo Layer: Layer 8 more phyllo sheets on top, brushing each with oil. Sprinkle mozzarella cheese evenly over these sheets.
Final Phyllo Layer: Layer remaining phyllo sheets (about 14) on top, brushing each with oil.
Bake: Bake for 60-75 minutes, until the top is deep golden brown and crisp, and the filling is hot and bubbly.
Rest & Serve: Let casserole rest for at least 15-20 minutes before slicing and serving.