Add the dried lentils and 1½ cups water to a medium pot. Bring to a boil, then cover and reduce to low heat. Simmer for about 25 minutes until softened and cooked through.

Combine the ground flaxseed and 3 tablespoons water in a small bowl. Set aside to thicken while the lentils cook.

Add the cooked lentils, flax egg, cremini mushrooms, shallot, garlic, bread crumbs, salt, black pepper, and oregano to a food processor. Blend on high until well combined.

Roll the mixture into 2-inch balls — about 20 total. Heat olive oil in a large skillet over medium-high heat and cook the meatballs, turning frequently, until evenly browned on all sides. Set aside.

In a large skillet over medium-high heat, melt 2 tablespoons of butter. Add the mushrooms and cook for 2 minutes. Add the garlic and cook for 1 minute more. Remove to a paper towel-lined plate and set aside.

To the same skillet, melt the remaining 2 tablespoons of butter over medium-high heat. Whisk in the flour, then whisk in the beef-style broth and white wine. Bring to a boil for 1 minute, then remove from heat.

Stir in the Dijon, sour cream, salt, black pepper, and nutmeg. Add the mushrooms back into the pan and stir gently to combine.

Prepare according to package directions. Before draining, reserve ½ cup of pasta cooking water. Add the reserved water a little at a time to thin the sauce to your preferred consistency.