Adjust an oven rack to about 6 inches from the bottom heating element of the oven, and heat the oven to 450ºF.

Meanwhile, peel 2 pounds carrots. Cut crosswise on a slight diagonal into 3-inch pieces (if they are more than 1-inch thick, halve them lengthwise).

Place 6 tablespoons cut unsalted butter in a 9x13-inch metal baking pan (do not use glass, as it can shatter). Bake until the butter is just melted, 3 to 5 minutes.

Remove the baking pan from the oven. Add the carrots, 4 smashed and peeled garlic cloves, 1 tablespoon minced fresh thyme leaves, 1 teaspoon kosher salt, and ½ teaspoon black pepper. Toss until well-coated. Arrange the carrots in a single layer cut-side down if they were halved. Roast until the bottoms begin to brown, 35 to 40 minutes.

A few minutes before the carrots are ready, whisk 1 ¼ cups low-sodium chicken broth and 1 teaspoon cornstarch together in a liquid measuring cup or small bowl until the cornstarch is suspended.

Remove the baking pan from the oven. Using a flat metal spatula or tongs, gently flip carrots. Re-whisk the broth mixture, then pour around the carrots.

Return the baking pan to the oven and roast until the carrots are tender and the sauce is thickened slightly, about 15 minutes.

Using a thin metal spatula or a slotted spoon, transfer the carrots to a serving platter. Stir the sauce in the baking pan to recombine, then spoon it over the carrots. Garnish with finely chopped fresh parsley leaves if desired.