Heat a stovetop grill pan over medium-high.
Drizzle oil on the cantaloupe, and place the slices on the grill. Grill the slices, without moving them, for about 30 seconds, or until browned on the first side. Flip the melon slices, and grill on the other side for an additional 30 seconds. Transfer to a cutting board to cool slightly.
Cut the melon slices into 1/2-inch pieces, and place them in a medium bowl. Add tomatoes, mint, 1/4 teaspoon of the salt, chili paste, and lime juice. Mix well; set aside to let the flavors mingle.
Meanwhile, heat 5 tablespoons of water in a large skillet over medium. Cut butter into 8 pieces. When bubbles just start rising to the water’s surface, begin adding the butter to the pan, 1 piece at a time, whisking constantly to form an emulsion. When all the butter is incorporated, reduce the heat to medium-low to keep the temperature just below a simmer. Add the thyme and the remaining 1/2 teaspoon salt, and swirl the pan to combine. Add the asparagus to the pan, and toss gently to coat it in the butter.
Cover the pan, and cook for 5 minutes, or until the asparagus is tender all the way through when pierced with the tip of a sharp knife. Transfer the asparagus to a platter, and spoon the melon salad on top. Scatter a few shavings of ricotta salata over the salad, if desired.
Adapted from Giada’s Italy. Copyright © 2018 by GDL Foods Inc. Published by Clarkson Potter/ Publishers, an imprint of Penguin Random House LLC.