Heat an oven-proof 12-inch skillet (I recommend cast iron) over medium-high heat until very hot.
Use a paper towel to pat the steak dry. Rub about ½ Tbsp oil on the steak and season with ½ tsp salt and ½ tsp pepper.
Place steak in hot skillet and let cook for 3 minutes. Flip and let cook for another 4-6 minutes, depending on desired doneness (I like to keep it rare/medium rare since it will be cooking more in the lasagna). Remove to a cutting board and let rest for 5 minutes before thinly slicing it against the grain.
Put remaining Tbsp of oil in the skillet and add peppers, onions, ¼ tsp salt, and ¼ tsp pepper. Cook for about 6 minutes until softened.
Add mushrooms and garlic to skillet and cook for another 3 minutes. Remove to a bowl and toss with the sliced steak. Keep skillet out.
Preheat oven to 400 degrees.
While oven is heating, making bechamel sauce. Add butter to a medium saucepan over low heat and let melt.
Sprinkle flour into melted butter and whisk, making sure to scrape the bottom of the saucepan to prevent burning. Cook for 3 minutes, until mixture is light golden and flour smell can't be detected.
Slowly pour milk into the roux, whisking constantly until there are no lumps. Let sauce simmer to thicken, about 5 minutes. Remove from heat and stir in parmesan cheese, remaining ½ tsp salt, ½ tsp pepper, cayenne.
Pour about ¼ cup bechamel sauce on the bottom of your skillet. Shingle 6 noodle halves around the skillet. Top with ½ the pepper and steak mixture, ½ cup grated provolone cheese, and about 1 cup of bechamel sauce.
Shingle 6 more noodle halves over the sauce and top with the remaining peppers and steak, ½ cup of grated provolone, and 1 cup of bechamel.
Top with remaining noodle halves, bechamel, and provolone.
Bake for 22-25 minutes, until lasagna is bubbling around the edges and the cheese is golden.
Top with chopped parsley before serving.