Preheat oven to 425°F. In large pot, heat oil over medium-high heat; cook mushrooms and ¼ tsp of the salt, stirring often, until softened, 10 to 15 minutes. Add 1 tbsp water; scrape up browned bits from bottom of pot. Add carrots and onion; cook, stirring occasionally, until onion is softened, about 4 minutes. Add garlic, thyme and hot pepper flakes; cook, stirring constantly, for 30 seconds.
Add broth; bring to boil. Reduce heat to medium-low; simmer, stirring occasionally, until carrots are softened, about 10 minutes. Remove thyme; discard. Stir in soy protein, parsley, peas and remaining salt; cook, stirring often, until mixture is warmed through, about 2 minutes. Scrape into 13x9 inch baking dish or six 10 oz ramekins.
Topping: In large bowl, combine squash, ¼ cup of the Parmesan, 3 tbsp of the butter and the salt. In small bowl, stir together Panko, remaining Parmesan and butter. Spread squash mixture over top of mushroom mixture; sprinkle with Panko mixture. Transfer to baking sheet; bake until Panko is dark golden and filling is hot, 25 to 30 minutes. Let stand for 10 minutes before serving with 2015 Chardonnay, St. David’s Bench Vineyard.