In a medium bowl, whisk egg yolks, egg, and Parmesan until completely smooth. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
In a Dutch oven or large skillet, heat olive oil over medium-high heat until pan is hot and olive oil is shimmery. Add mushrooms to pan and saute, stirring mushrooms occasionally until they are lightly-browned and tender (about 3-5 minutes)
Add shallot, garlic, and tomatoes to mushrooms and saute an additional 1-2 minutes until fragrant and a light golden brown. Season mushrooms with salt and pepper to taste.
Bring a pot of lightly-salted water to a boil and cook pasta until just barely al-dente. Reserve 1-1/2 cups pasta cooking water and drain pasta.
Add pasta and 1/2 cup reserved pasta water to mushroom mixture. Cook over medium heat 2-3 minutes until liquid is absorbed. Remove from heat and allow to cool 2 minutes.
Whisk remaining 1/4 cup pasta water into egg yolks until sauce is completely smooth. Fold egg sauce into pasta mixture, stirring constantly with a wooden spoon until a creamy sauce forms and coats pasta. (drizzle in additional pasta water if needed to loosen sauce)
Stir parsley into carbonara and season with additional salt and pepper if needed. Serve carbonara immediately while hot with additional Parmesan grated on top. Enjoy!