In a large pot of boiling salted water, cook pasta according to package directions. Drain and set aside.
Coat both sides of the steak with oil and season generously with salt and pepper. On a grill or grill pan over medium-high heat, cook the steak until your desired doneness (see below) using a thermometer. Transfer to a plate to let rest.
Add butter to the same pan over medium heat and let it melt, then add garlic and cook until fragrant, 1 minute. Whisk in the flour and stir together cooking 1 minute more, then add milk and simmer until thickened, 5 minutes. Add blue cheese and season with salt and pepper to your desired taste.
Add cooked pasta and spinach to the sauce and toss until the spinach is wilted.
Slice the steak against the grain and serve over the top of the pasta with toasted bread on the side. Garnish with parsley.