Wipe away any dirt from mushrooms. Remove hard stems and slice. Trim ends off the pearl onions and peel. Cut big ones in half. Slice leek in half lengthwise and chop. Chop carrots and set aside.
Heat a dutch oven over medium high heat. Add 1 tbsp butter and 1 tbsp olive oil. Add half of the mushrooms and all of the onions. Don’t disturb the mushrooms or onions for a few minutes and then stir to combine. Season with salt, cracked pepper and 1/2 tsp fresh thyme. Once mushrooms are browned, transfer mushrooms only to a bowl using a slotted spoon. Add butter and oil to the pan again with remaining mushrooms. Cook the same way and once done, transfer to the bowl.
Add 1 tbsp olive oil to the pan with leeks, garlic and carrots. Cook for several minutes. Add tomato paste and cook for 1 minute. Add flour and cook for 1 minute more. Add all the liquids to a glass measuring cup and whisk to combine. Pour liquids into the pot, scraping up any browned bits off the bottom. Toss mushrooms and onions into the pot with remaining thyme sprigs and bay leaf. Cover the pot loosely with the lid and simmer for 30 minutes. If the mixture isn't thick enough, create a slurry with 1 tsp cornstarch and 2 tbsp water. Stir in a separate small bowl until fully combined and stir into mushrooms. Mixture should thicken in no time.
*Macros are provided as an estimate for convenience. Your final numbers will vary depending on ingredient brands, substitutions, and how you portion the recipe.