Position a rack in the center of the oven and heat the oven to 350°F. Butter a 9x13-in. (or similar) baking dish. In a 12-in. skillet, heat the oil over medium-high heat. Add the onion and 1/2 tsp. salt and cook, stirring occasionally with a wooden spatula, until golden-brown, 7 to 10 minutes.
Meanwhile, melt the butter and pour into a medium bowl. Add the panko, parsley, and thyme and toss well.
Whisk the heavy cream, mustard, 1-1/2 tsp. salt, and 1/4 tsp. pepper into the onion, scraping up any browned bits, and then stir in the carrots. Bring just to a boil, cover, lower the heat to medium low, and simmer until the carrots are crisp-tender, 10 to 12 minutes.
Spread the carrot mixture evenly in the prepared dish. Scatter the Cheddar over the carrots, top with the panko mixture, and bake until the carrots are tender when pierced with a fork and the crumbs are golden-brown, 30 to 40 minutes.
Let rest for 15 minutes before serving.