Preheat your oven to high broil with your rack set to the top of the oven.
Start by making your brown butter. Simply melt your butter over medium heat using a small saucepan with a light-colored bottom so you can keep track of the color. Swirl or stir often to make sure the butter is cooking evenly. As the butter melts, it will begin to foam, turn golden brown and smell nutty. Pour the brown butter into a large mixing bowl
Spread your shishito peppers out in a single layer on a broiler proof baking sheet. Broil the peppers until they are lightly blistered and just starting to soften. It helps to toss the peppers occasionally to make sure they are blistered evenly. Total broiling time is roughly 5-8 minutes.
Transfer the peppers to your large mixing bowl with the brown butter and toss lightly with the lemon juice, Parmesan cheese, lemon zest and salt.
