- Preheat the oven to 425°F (220ºC). Line a baking sheet with parchment paper or a silicone baking mat. Spread out the carrots on the sheet and lightly spray with olive oil.
- Sprinkle with the dried thyme, dried parsley, and salt and pepper. Toss to coat. Roast for 25 minutes, or until caramelized and tender. Set aside until ready to use.
- Once the carrots are in the oven, bring the water to a boil in a medium pot, then remove from the heat. Add the dried mushrooms and set aside.
- Melt the butter in a large shallow saucepan over medium heat. Add the onion and sauté until translucent. Add the garlic, rosemary, and fresh thyme and cook until fragrant, about 2 minutes. Add the button and wild mushrooms.
- Use a slotted spoon to scoop the rehydrated mushrooms from the water into the pan (do not discard the water). Cook for 8 to 10 minutes, stirring occasionally, until the mushrooms are tender but still hold their shape.
- Add the oat flour and cook, stirring constantly, until the flour is fully incorporated. Add the wine and cook, stirring frequently, until the liquid has reduced.
- Add ½ cup of the reserved mushroom soaking water, bring to a boil, then reduce to a simmer. Cook for about 5 minutes, until most of the liquid has been absorbed.
- Add the carrots, lemon juice, salt, and pepper and remove from the heat. Serve over creamy polenta, garnished with fresh parsley, if desired. Leftovers will keep in an airtight container in the fridge for 2 to 3 days.