Boil a large pot with boiling salted water and cook the pasta according to the package instructions. Before draining, reserve 1/2 cup pasta water. Put pasta back in the pot.
Drizzle both sides with oil, and season with salt and pepper. Cook steak on medium heat for 4 minutes per side. Let rest on a plate for 10 minutes. Slice steak thinly.
In skillet, melt butter over medium heat. Stir in garlic and cook for 1 to 2 minutes. Mix in flour, cook for 1 minute, then add milk slowly, whisking to break down lumps. Let simmer until thickened, about 5 minutes. Season with salt and pepper. Cook tomatoes until they burst, about 2 to 3 minutes
Add the cooked pasta to a skillet with 1/4 cup of reserved pasta water. Toss until combined, adding more pasta water if necessary. Toss in the spinach until it is wilted.
Top the steak with balsamic glaze and top with sliced vegetables.