Clean the asparagus. Rinse the asparagus under cool running water to remove any debris. Then, gently pat dry the spears with a clean kitchen towel or paper towels.
Trim the asparagus. Hold each asparagus spear by the tough end and bend it until it naturally snaps off. This removes the woody part. Alternatively, you can cut off about 1-2 inches from the ends using a sharp knife. If the asparagus is thick, consider using a vegetable peeler to remove any tough outer skin from the lower part of the stem.
Heat the skillet: In a large nonstick skillet, heat some olive oil over medium-high heat.
Saute the asparagus. Fry asparagus for 3-4 minutes. Stir frequently to ensure even cooking. The asparagus should turn bright green and become tender.
Add the peas. Stir in the peas and cook for an additional 1-2 minutes. If using frozen peas, you can thaw them slightly by placing them in a warm bowl of water beforehand.
Season and serve. Season the dish with salt, black pepper, and a drizzle of lime juice, if desired. Serve the sautéed asparagus and peas warm as a side dish. For added flavor, top it off with fresh basil, a squeeze of lemon juice, and a sprinkle of grated Parmesan cheese. Enjoy!