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.