4 tablespoons extra-virgin olive oil, divided 5 garlic cloves, coarsely chopped 1 3-ounce package thinly sliced prosciutto, cut crosswise into strips 8 large eggs 1 9.5-ounce package thin soba noodles 1 pound asparagus, ends trimmed, cut on sharp diagonal into 1/8-inch-thick slices 1 cup freshly grated Parmesan cheese plus additional cheese shavings
Heat 2 tablespoons extra-virgin olive oil in large skillet over medium-high heat. Add garlic; stir 30 seconds. Add prosciutto strips; cook until slightly crisp. Remove from heat. Set aside.
Heat 1 teaspoon oil in each of 2 nonstick skillets over medium heat. Crack 4 eggs into each skillet. Cook on 1 side until eggs begin to set, about 2 minutes. Remove from heat. Cover; set aside.
Cook soba noodles in large pot of boiling salted water 5 minutes, stirring occasionally. Add sliced asparagus to pot; cook until noodles are cooked through and asparagus is just tender, 2 to 3 minutes. Drain noodles and asparagus, reserving 1 cup cooking liquid.
Add drained noodles and asparagus to prosciutto mixture in skillet. Cook over medium heat until heated through, tossing and adding reserved cooking liquid by 1/4 cupfuls to moisten.
Remove skillet from heat. Add grated Parmesan cheese and remaining 1 tablespoon plus 1 teaspoon olive oil and toss to coat. Divide among 8 plates. Top each serving with 1 egg and cheese shavings. Serve immediately.