Put the olive oil in a large ovenproof skillet over medium heat. Trim, peel, and chop the onion. Add the onion to the skillet and cook, stirring occasionally until it’s softened, 3 to 5 minutes.
Raise the heat to medium-high. Add the arugula to the softened onion, a handful at a time, and sprinkle with salt and pepper. Stir and cook until the arugula is just wilted and the liquid is evaporated, 5 to 10 minutes.
Crack the eggs into a medium bowl. Add the parmesan, sprinkle with salt and pepper, and beat the mixture with a fork or whisk. Turn the broiler to high; put the rack 4 inches from the heat.
When the arugula is ready, add the peas, herbs, and a sprinkle of salt and pepper. Stir to combine and turn the heat to low. Pour the eggs into the skillet, tilting it or using a spoon to distribute them evenly. Cook until the eggs are barely set, 5 to 10 minutes.
Transfer the skillet to the broiler and cook just until the eggs turn golden, a minute or 2. Cut the frittata into wedges and serve, hot, warm, or at room temperature.