Start the skillet: Set a large deep skillet with a lid over medium heat. Keep the lid nearby so it is ready when you add the eggs.

Add 2 tablespoons olive oil to the skillet. When the oil looks loose and shiny, add the chopped onion.

Cook the onion for 4 to 5 minutes, stirring often, until it softens and starts to look translucent. Season it with a small pinch of salt.

Add the sliced garlic to the skillet. Stir for 30 seconds, just until it smells fragrant.

Add the dry orzo to the skillet. Stir for 1 minute so the pasta is lightly coated in the oil and onion.

Pour the vegetable broth and 1/2 cup water into the skillet. Stir well and scrape the bottom of the pan so no pasta sticks there.

Bring the liquid to a gentle simmer over medium heat. Once it starts bubbling, lower the heat to medium-low.

Cook the orzo uncovered for 6 minutes, stirring every minute or two. It should start to swell and the liquid should look a little creamy, not dry.

Add the frozen peas to the skillet. Stir them into the orzo and cook for 2 minutes, until the peas are hot and the orzo is nearly tender.

Stir 1/3 cup of the grated Parmesan into the skillet. Add 1 tablespoon lemon juice and stir until the cheese melts into the sauce.

Taste the orzo and add more salt if it needs it. If the skillet looks thick or tight, stir in 2 to 4 tablespoons water so the orzo stays loose and creamy.

Add the eggs: Use the back of a spoon to make 4 shallow wells in the orzo. Space them out around the skillet so each egg has room.