Cut squash in half vertically and scoop out seeds. Cut halves into 1/2-inch-thick wedges. Trim and discard the peel from each wedge. In a 12- by 17-inch baking pan, mix squash with 2 tablespoons olive oil and the thyme until coated. Sprinkle generously with salt and pepper. Arrange pieces in a single layer. Bake in a 475° oven until squash is slightly browned and tender when pierced, 15 to 20 minutes.
Meanwhile, in a small bowl, whisk together vinegar, remaining 2 tablespoons oil, and 1/4 teaspoon salt. Place greens and squash in a large bowl.
In a 10- to 12-inch frying pan over medium-high heat, stir bacon until lightly browned and crisp, about 5 minutes. Transfer to paper towels to drain. Discard all but 2 tablespoons fat from pan. Add shallots to pan and stir constantly over medium-high heat until limp, about 4 minutes. Remove from heat and carefully stir in olive oil mixture. Pour mixture evenly over greens and squash; mix gently to coat.
Divide salad among six plates. Using a vegetable peeler, shave pecorino cheese over the top of each. Sprinkle salads evenly with bacon and candied pepitas. Add more salt and pepper to taste.
A.O.C. and Lucques, Los Angeles, CA
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