Heat a stove-top grill pan or griddle with cooking spray and set over medium-high heat to preheat. Season both sides of flank steaks with salt, black pepper, garlic powder, and onion powder. Place steaks on hot pan and cook 5 minutes per side for medium meat. Let steaks rest 10 minutes before slicing crosswise into 1/4-inch thick slices.
While the steaks are cooking, season both sides of polenta with salt and black pepper. Arrange slices alongside steak for the last few minutes of cooking; cooking slices 1 to 2 minutes per side, until golden brown.
While the steak and polenta are cooking, heat oil in a large skillet over medium-high heat. Add pearl onions and cook 3 minutes, until golden brown stirring with a spoon. Add mushrooms and cook 3 minutes, until mushrooms soften. Add thyme and cook 1 minute, until fragrant. Add wine and bring to a simmer, for 5 minutes, until sauce reduces to 1/4 cup.
Serve half of the steak over toasted polenta slices with all of the onion-mushroom mixture spooned over top. Reserve remaining steak for sandwiches.