Preheat the broiler with an oven rack set about 4 inches from the heat source. Have a large mixing bowl ready.
Melt the butter in a small saucepan over medium heat until light brown specks start to form and the butter starts to smell nutty, swirling the pan occasionally, about 5 minutes. Pour immediately into the mixing bowl, being sure to scrape the brown bits from the bottom of the pan.
Spread the shishito peppers in a single layer on a baking sheet. Broil the peppers until lightly blistered and just starting to soften, shaking the baking sheet occasionally, 3 to 5 minutes.
Transfer the hot peppers to the bowl with the browned butter. Lightly toss with the lemon juice, cheese and a sprinkle of salt. Serve immediately.
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