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Step 1
Bring a large pot of salted water to a boil.
Step 2
Season steak with salt and pepper to taste.
Step 3
For the caramelized onions: cut onions in half and thinly slice short end. Add 1 tbsp olive oil to a nonstick skillet and add the onions. Add salt, paprika, and balsamic vinegar and cook on medium-low to low heat until onions are tender, transparent, and slightly brown, about 30 to 35 minutes, stirring occasionally.
Step 4
Meanwhile, cook pasta according to package directions. Drain and set aside in a large work bowl and let cool.
Step 5
While the pasta is cooling, heat a grill pan over high heat and spray with cooking spray or preheat the broiler to high.
Step 6
Cook the steaks about 3 to 4 minutes on each side for medium rare, or longer to your desired likeness (until a thermometer inserted in the center registers 145°F for medium rare, 160°F for medium, or 165°F for well done.)
Step 7
Let stand for 10 minutes, then slice into thin strips.
Step 8
Add the arugula, 4 teaspoons olive oil, 1 1/2 tbsp balsamic, salt and pepper to the bowl with the pasta and toss.
Step 9
Add the caramelized onions, toss well and divide between four plates, about 1 1/2 cups each. Top each with 3 oz steak and shaved Parmesan. Eat right away.