To make the braised beef, in a large pot over medium-high heat, melt the butter with 1 tablespoon of the olive oil. Arrange the meat in the pot in a single layer and season with salt and pepper. Cook, turning occasionally, until browned on all sides. 

Add the onions and garlic to the pot and cook, stirring occasionally, until the onions are softened. Add the flour and stir to coat the meat. Add the wine, bay leaves and thyme, and season with salt and pepper. Bring to a boil, then cover the pot and reduce the heat so the mixture simmers. Cook until the meat is tender, about 1 hour.

In a large fry pan over medium-high heat, warm the remaining 1 tablespoon olive oil. Add the mushrooms, celery and carrots and cook, stirring occasionally, until tender and nicely browned, about 10 minutes.

To make the noodles, in a large bowl, stir together the flour and salt. Add the eggs, milk and butter. Knead the dough until smooth, about 5 minutes. Cover the bowl and let the dough rest for 10 minutes. 

On a floured surface, roll out the dough 1/4 inch thick. Using a sharp knife, cut the dough into the desired length. 

Bring a large pot of salted water to a boil over high heat. Add the noodles and cook until al dente. Drain well and transfer to a large bowl. Toss the hot noodles with butter to coat.

To serve, stir the mushroom mixture into the stew and spoon over the noodles. Garnish with a little chopped parsley.