Pat the pork medallions dry. Season with salt, pepper, smoked paprika, and thyme, then dust lightly with flour on all sides.

Bring a large pot of salted water to a boil for the noodles. Cook the egg noodles until just tender, then drain and toss with 1 tablespoon butter so they stay glossy.

While the noodles cook, heat the olive oil and 1 tablespoon butter in a large skillet over medium-high heat until shimmering. Sear the pork in a single layer, working in batches if needed, 2 to 3 minutes per side until browned. Transfer to a plate.

Reduce the heat to medium. Add the mushrooms and cook, stirring occasionally, until they release their moisture and begin to brown, about 5 minutes.

Add the shallot and cook for 1 minute, then stir in the garlic for 30 seconds until fragrant.

Pour in the red wine and scrape up the browned bits from the pan. Simmer until reduced by about half, 2 to 3 minutes.

Add the chicken broth, Dijon mustard, and Worcestershire sauce. If using trimmed green beans, stir them in now. Simmer 4 to 6 minutes, until the sauce slightly thickens and the green beans are crisp-tender, then stir in the cream.

Return the pork and any juices to the skillet. Simmer gently over medium-low heat until the pork reaches 145°F and the sauce lightly coats the spoon, about 3 to 5 minutes. If using frozen peas, stir them in during the last 2 minutes just to heat through. Remove from the heat and let the pork rest in the sauce for 3 minutes.

Taste and adjust with extra salt, pepper, or a squeeze of lemon juice if you want a brighter finish.

Serve the pork and sauce over the buttered noodles, topped with parsley and Parmesan if using.