Season steaks with ¼ teaspoon salt and pepper. Set to one side and allow to come to room temperature.
In a pot of boiling water, cook spaghetti until al dente. Drain, reserving 5 tablespoons of pasta water for the pesto.
Meanwhile, place pesto ingredients in a blender and blitz until smooth, adding reserved pasta water. Add to pasta and toss to coat evenly. Add tomatoes and rocket. Season and toss once more.
Set a griddle or non-stick pan over a high heat. Add steaks and cook for 1-2 minutes either side, or until your liking. Remove from pan and rest.
Divide pasta among plates. Slice steak and place on top of pasta. Garnish with extra basil leaves and freshly ground black pepper.