Preheat oven to 425 degrees F with rack in center position.
Cut Delicata squash in half lengthwise and use a spoon to remove seeds and stringy pulp. (Set aside if planning to roast the seeds, otherwise, discard.)
Cut each half, crosswise, into 1/4-inch thick slices. Arrange on a baking sheet, toss with 2 tablespoons olive oil, thyme sprigs, and a few pinches of kosher salt and pepper. Roast 30-40 minutes, turning squash slices halfway through, until tender and golden.
Make the vinaigrette and serve
In a small saucepan, simmer apple cider vinegar until reduced to 2-3 tablespoons, about 2-3 minutes. Transfer to a small bowl and set aside.
In the same saucepan, heat butter over medium-low heat, gently swirling the pan occasionally, until solids are light golden brown and fragrant. Remove from heat.
Stir shallots, honey, red pepper flakes, and a pinch of kosher salt into the reduced cider vinegar. Slowly whisk 1 tablespoon olive oil and browned butter into the vinegar mixture until emulsified.
In a large bowl, gently toss together spinach, roasted Delicata squash, and vinaigrette until coated. Season to taste with salt and pepper. If desired, garnish with roasted squash seeds or toasted nuts. Serve immediately, while the dressing is still warm.
For the best flavor and presentation, this salad should be served immediately after assembling, as the spinach leaves will lightly wilt from the roasted squash slices and warm vinaigrette. I like to serve the salad lightly-dressed to allow the flavors of the squash and spinach to shine through, but if you prefer more dressing, the vinaigrette is easily doubled.
To roast Delicata squash seeds:
Preheat oven to 325 degrees F. Rinse seeds in a bowl of water and discard stringy pulp (seeds will float to the top of the water as separated).
Add seeds and 1 teaspoon salt for every 1/2 cup seeds to a small saucepan. Add enough water to cover by 1 inch and bring to a boil. Simmer for 5-7 minutes and drain seeds into a colander. Let cool slightly and dry with a paper towel.
Place seeds onto a baking sheet and toss with about a teaspoon of olive oil (or another neutral oil) to coat and a few pinches of kosher or sea salt. Arrange seeds in a single layer and roast for about 10 minutes.
Stir seeds, and continue roasting for 5-10 minutes, until lightly toasted and fragrant. (Seeds should not be dark brown.) Let cool and enjoy.