Asparagus with Grilled Melon Salad

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1/2 small cantaloupe melon, peeled, seeded and cut into 1/2-inch slices

1 tablespoon olive oil 

1 cup cherry tomatoes, quartered 

1 tablespoon chopped fresh mint 

2 teaspoons lime juice 

1 teaspoon Calabrian chile paste 

Kosher salt

1 stick (8 tablespoons) unsalted butter, cold, cut into 8 pieces

2 sprigs fresh thyme, leaves stripped 

1 pound asparagus, trimmed

Ricotta salata, shaved with a vegetable peeler, for serving, optional