Place a baking sheet in the upper third of the oven and another in the lower third; preheat to 450˚. Toss the squash, carrots, olive oil, thyme, 1 teaspoon salt and a few grinds of pepper in a large bowl. Put the squash on one of the baking sheets and the carrots on the other, spreading the vegetables in a single layer. Roast, switching the pans halfway through, until the vegetables are lightly browned and tender, 25 to 30 minutes.
Meanwhile, mix the cream cheese with the dill in a small bowl. A few minutes before the vegetables are done, toast the bread, then spread with the cream cheese mixture. Toss the spinach with the vinegar and season with salt and pepper.
Lay out 4 slices of bread, cream cheese–side up. Top each with a layer of beets, then the squash, carrots, spinach and another slice of bread. Cut in half.