Using an electric mixer, beat butter and Parmesan until creamy.

In a large pot of boiling salted water, cook fettuccine according to package instructions until al dente, about 12 minutes. Reserve about 1/2 cup of cooking water; drain pasta.

Return fettuccine to warm pot. Toss pasta with 1/2 teaspoon salt, cheese mixture, and 1/4 cup of the pasta water. Add more pasta water, as needed. Serve with additional cheese

Heat butter and 2 tablespoons oil in a large nonstick skillet over medium-high. Add leeks, season with salt and pepper, and cook, stirring often, until translucent, 3 to 4 minutes. Stir in asparagus and 1/2 cup water. Reduce heat to low, cover, and cook until asparagus is bright green and just tender, 3 to 4 minutes. Uncover, increase heat to high, and cook until most of liquid has evaporated, about 1 minute. Transfer to a bowl.

Return skillet to high heat; swirl in 1 tablespoon oil. Spread rice in a single layer; cook, undisturbed, until crisp in places, about 4 minutes. Stir in leek mixture, lemon zest and juice, peas, cheese, and herbs. Season with salt and pepper. Serve with more cheese and herbs, topped with a fried egg.