Heat 2 tablespoons of olive oil in a large skillet over medium-high heat until it shimmers. Add the sliced steak and cook for 3-4 minutes until just browned. The beef should still be slightly pink since it'll continue cooking in the oven. Remove to a plate and set aside.

In the same skillet, add remaining olive oil along with the sliced peppers and onions. Cook for 8-10 minutes, stirring occasionally, until the vegetables soften and develop golden edges. Add minced garlic during the last minute until fragrant without browning.

Preheat your oven to 375°F. In a large mixing bowl, whisk together softened cream cheese and heavy cream until smooth. Stir in salt, pepper, and paprika, then add 1½ cups of the provolone cheese, reserving the rest for topping.

Grease a 9x13 inch baking dish with butter or cooking spray. Layer the cooked beef evenly across the bottom, followed by the sautéed pepper and onion mixture. Pour the creamy cheese mixture over everything, using a spatula to ensure even distribution.

Sprinkle the remaining provolone and all the mozzarella evenly over the top.

Bake for 20-25 minutes until the cheese is golden and bubbling around the edges. A knife inserted in the center should come out hot and the casserole should feel set but not rigid. Let it rest for 5 minutes before serving.