Begin by preheating the oven to a temperature of 375°F (190°C). Subsequently, apply a thin coat of cooking spray to a 9x13-inch casserole dish and place it aside.

In a suitably sized mixing bowl, meticulously combine the Bisquick mix, milk, egg, and half the quantity of black pepper. Once combined, transfer the Bisquick mixture into the earlier prepared baking dish.

Utilizing a large skillet, heat it over medium-high temperature. Once hot, add the ground beef. Cook the beef for approximately 5-7 minutes or until it achieves a browned appearance.

Following this, introduce the sliced onions and green bell peppers to the skillet containing the beef. Continue the cooking process for an additional 5-7 minutes or until the vegetables have softened. Ensure to drain any surplus grease from the skillet.

Carefully integrate the brown gravy mix, water, and the remaining half of the black pepper into the beef mixture in the skillet. Allow it to simmer for approximately 3-5 minutes, or until a reduction in the liquid is observed.

Proceed to evenly distribute the beef mixture over the Bisquick layer in the baking dish. Subsequently, overlay the mixture with the slices of provolone cheese, ensuring they are evenly spaced.

Place the casserole dish into the preheated oven and bake for a duration of 25-30 minutes. Ensure that the provolone cheese acquires a golden brown hue and that a toothpick, when inserted into the Bisquick layer, emerges clean. Should the cheese layer brown too rapidly, it is advisable to cover the casserole with aluminum foil.

Post baking, permit the casserole to cool for a duration of 10 minutes prior to serving.