Broccoli Cheddar Potato Gratin

Wash your hands and clean the work surface. Heat the oven to 400°F with a rack in the center. Grease the baking dish with 1 tablespoon of the butter. Scrub the potatoes and rinse the broccoli under running water, trim away damaged areas, and pat dry. Slice the unpeeled potatoes evenly into 1/4-inch rounds. Cut the broccoli into roughly 1 1/2-inch florets. Mince the garlic and grate the cheddar, keeping the sauce and topping portions separate.

Bring the 3 quarts of water and 1 teaspoon of the salt to a boil in the large pot. Add the broccoli and blanch for 1 minute, just until bright green but still firm. Lift it into the colander with a slotted spoon, leaving the cooking water in the pot. Briefly rinse the broccoli under cold running water to stop the cooking. Drain thoroughly, pat away excess moisture with the clean towel, and transfer to the baking dish.

Return the water to a boil and add the potatoes. Reduce the heat to maintain a gentle simmer and cook for 8–12 minutes, checking early and separating any slices that stick together. A thin knife should enter a slice with only slight resistance; the potatoes should be nearly tender but still hold their shape. Drain gently and let steam-dry in the colander for 2 minutes, then add to the baking dish.

Melt the remaining 4 tablespoons butter in the saucepan over medium heat. Add the garlic and cook for 30 seconds without browning. Whisk in the flour and cook, whisking constantly, for 2 minutes, until the mixture is smooth and lightly bubbling.

Gradually whisk in the milk, starting with a small splash and whisking smooth before adding more. Bring to a gentle simmer, stirring frequently and scraping the bottom and corners of the pan. Simmer for 3–5 minutes, until smooth and thick enough to coat the back of a spoon while still pouring easily.

Remove the saucepan from the heat. Stir in the mustard, remaining 1 teaspoon salt, and pepper. Add the 8 ounces of cheddar reserved for the sauce in small handfuls, stirring until melted before adding the next handful. Do not return the cheese sauce to a boil.

Pour the sauce over the potatoes and broccoli. Gently fold with the spatula to coat everything without breaking the potato slices, then spread into an even layer. Scatter the reserved 2 ounces of cheddar evenly over the entire gratin.

Bake uncovered for 25–30 minutes, until the sauce is bubbling in the center, the top is golden in patches, and a knife slides easily through the potatoes. Check that the center of the gratin reaches 165°F (74°C) with a food thermometer, measuring without touching the baking dish. Continue baking if that temperature has not been reached. If the top browns before the potatoes are tender, move the dish to a lower oven rack and continue baking until tender.

Using oven mitts, transfer the dish to a heatproof surface. Rest for 10 minutes so the sauce settles before dividing into six portions.