Heat 1 tablespoon neutral oil in a large skillet over medium-high heat. Add the very thinly sliced steak and cook for 2–4 minutes, stirring, until just cooked through; remove it from the skillet and chop it into small pieces if needed.

Add the diced onion, green bell pepper, and mushrooms to the same skillet. Cook for 5–7 minutes, stirring occasionally, until the vegetables soften and most of their moisture has evaporated, then add the minced garlic and cook for about 30 seconds.

Return the beef to the skillet and stir in the Worcestershire sauce, kosher salt, and black pepper. Remove the skillet from the heat and let the filling cool for 5–10 minutes.

Heat the oven to 425°F (220°C). Line a baking sheet with parchment paper and lightly coat it with cooking spray, or place a wire rack over the sheet for extra airflow and crispness.

Place one egg-roll wrapper on a work surface with a corner pointing toward you. Put approximately 1/3 cup of filling across the lower third of the wrapper and top it with about 1/2 ounce of provolone.

Fold the bottom corner over the filling, then fold both side corners inward. Roll the wrapper tightly toward the remaining corner, brush that final corner with water, and press to seal.

Arrange the finished egg rolls seam-side down on the prepared baking sheet. Lightly brush or spray the tops and sides with oil so the wrappers brown evenly in the oven.

Bake for 18–22 minutes, turning the egg rolls once halfway through the cooking time. Remove them when the wrappers are golden brown and crisp, then serve hot with your favorite dipping sauce.