Position a rack in the center of the oven and heat the oven to 425ºF.
Toss the parsley, lemon zest, and garlic in a bowl, cover with plastic wrap, and set aside (this is the gremolata).
Peel the carrots and slice in half lengthwise. If they’re big, slice each half lengthwise again into long quarters. Put the carrots on a large rimmed baking sheet and toss with the shallots, thyme, olive oil, salt, and several grinds of pepper. Arrange the carrots in a single layer.
Roast the carrots, tossing occasionally, until they are tender and ever so slightly browned, 20 to 30 minutes. Remove from the oven and toss in the olives and the gremolata. Adjust the seasoning with salt and pepper to taste.