Place a baking sheet in the oven; preheat to 450 degrees F. Toss the carrots with 1 tablespoon olive oil, a big pinch of salt and a few grinds of pepper in a large bowl. Spread the carrots on the hot pan and bake until lightly browned and tender, 20 to 25 minutes.
Meanwhile, toast the almonds in a small dry skillet over low heat, stirring frequently, about 5 minutes. Let cool.
Whisk the vinegar, honey, mustard and shallot in a large bowl. Slowly whisk in the remaining 1/4 cup olive oil until combined. Add the spinach, lettuce and almonds and toss to coat. Season with salt and pepper. Transfer the salad and carrots to a platter. Top with the goat cheese and chives.