Preheat oven to 425°.
Cut potatoes into about 6-8 wedges per potato. Place them on a sheet pan. Sprinkle with cumin, ½ tsp salt, and ¼ tsp pepper. Toss with 1 tbsp olive oil and spread out on sheet pan. Bake until browned and crisp, about 30 minutes, flipping halfway through.
Meanwhile, separate oyster mushrooms and, if large, cut or tear into strips. Thinly slice yellow onion and bell pepper.
Heat 2 tbsp olive oil in a large skillet over medium-low heat.
Add oyster mushrooms, yellow onion, bell pepper, and a pinch of salt and pepper to the skillet. Cook 12-15 minutes, stirring occasionally, or until tender and browned.
Remove skillet from heat. Add soy sauce and vinegar and stir to combine. Spread mixture into and even layer and top with provolone cheese. Allow cheese to melt (place pan over low heat to speed it up). Leaving it to melt.
Spread mayo on the hoagies and toast in the oven for about 3-5 minutes.
Fill hoagies with cheesy mushroom filling. Serve sandwiches with a side of potato wedges.