Season steaks with salt and black pepper. On a grill pan coated with cooking spray, cook steaks over medium-high heat, turning once, until pink inside, 3 to 4 minutes per side. Remove from heat and cover with foil. In a bowl, toss carrots, squash, pearl onions and sprouts in 1/2 tablespoon oil. Over medium heat, in batches and turning once, cook until soft and seared, 6 minutes. In a large pan over medium heat, heat remaining 1 1/2 tablespoons oil. Slice mushrooms; to pan, add mushrooms, white onion and garlic; cook until onion browns, 5 to 7 minutes. Add wine and simmer 3 to 5 minutes. Add broth and bring to a boil. In a bowl, dissolve cornstarch in 1 tablespoon cold water. Reduce heat and slowly add cornstarch mixture to broth mixture, stirring constantly, until sauce is thick enough to coat the back of a spoon. Add tomato paste, Italian seasoning and salt and black pepper; simmer 7 to 10 minutes. Slice steak, top with mushroom sauce; serve alongside vegetables.
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