Heat the oven to 425 F / 220 C with a 33 x 46 cm / 13 x 18 inch rimmed sheet pan on the middle rack. The pan needs to preheat with the oven.

Trim the tops and root tails off the radishes. Halve them lengthwise, and quarter any piece wider than 4 cm so everything is about the same size. Pat the cut radishes dry with a clean towel.

Melt the duck fat in a small bowl, about 20 to 30 seconds in the microwave if it's solid. Toss the radishes in a large bowl with the fat, thyme, salt, and pepper until every piece is glossy.

Carefully pull out the hot pan and tip the radishes onto it, cut side down, in a single layer. They should sizzle. Roast for 15 minutes, until the cut sides are starting to brown.

Scatter the smashed garlic over the pan and stir the radishes with a spatula. Roast for 10 more minutes, until the edges are browned and a knife tip slides in easily. Don't add the garlic any earlier, because it turns dark and bitter over a full 25 minutes.

Squeeze the lemon juice over the radishes and sprinkle with the parsley. Serve hot, straight from the pan.