Place the porcini in a small bowl and cover them with ⅔ cup hot water. Set aside.
Heat 1 tablespoon of oil on medium-high in a large saucepan. Add the pearl onions and cook for 5-6 minutes, stirring occasionally. Remove them from the pan and set aside.
Melt 1 tablespoon of butter in the pan, add the cremini mushrooms in a single layer, and stir quickly to coat. Cook them for 6-7 minutes until browned. Do not stir often. Remove them from the pan and set aside.
Add 1 tablespoon of oil, lower the heat to medium, add the carrots and white onion and saute for 6-7 minutes, stirring occasionally. Add the garlic and saute for 2 more minutes.
Meanwhile, strain and roughly chop the porcini, reserving the liquid.
Add the wine, broth, strained porcini water, chopped porcini, tomato paste, thyme, oregano, salt, and pepper, and bring the liquid to a boil. Lower the heat immediately and let it simmer on low for 20 minutes.
Meanwhile, use a fork to mix the flour and 1 tablespoon of butter into a paste.
Add the flour and butter mixture to the pot and stir well until it's evenly incorporated.
Return the pearl onions and cremini mushrooms to the pot and simmer for an additional 10 minutes until the contents reach the consistency of a thick stew. Taste and adjust for salt and pepper.
Serve immediately over egg noodles with a sprinkling of fresh parsley.