Add the carrots and onions to the oil and cook for 10 minutes, stirring occasionally, until the aromatics begin to deepen in color and develop a crust. Season with salt and pepper and move them to one side of the pot.
If desired, melt 2 tablespoons butter into the pot.
Add the mushrooms and cook, stirring regularly, for 12-15 minutes until they release all their liquid and the liquid evaporates. It will take some time, so be patient. Continue cooking until the mushrooms develop a beautiful golden crust.
Add the garlic to the pot and cook for 1 minute until fragrant. Season with salt, white pepper, and thyme and cook for 45 seconds until fragrant.