Position rack in hottest area of oven. Preheat oven to 425°F/220°C.

Halve the potatoes if necessary; some might be small enough to leave whole. Steam or cook in boiling water for 10 to 12 minutes; drain. They will not be cooked through but should be about halfway cooked. Cool slightly and place in large mixing bowl.

Meanwhile, remove any feathery fronds from the fennel bulb and save, setting aside. Cut the stalks very thinly, crosswise into 1/8-inch (3 mm) rounds; set aside in a small bowl and stir together with 1 tablespoon lemon juice and season with salt and pepper; save for later.

Remove and discard root end of fennel bulb, then cut bulb into sixths and add to mixing bowl holding potatoes. Toss with oil, then spread out in single layer on a rimmed half-sheet pan and roast for about 15 minutes or until tender and cooked through.

While potatoes and fennel are roasting, prepare the cucumber as follows: grate, skin and all, on the largest holes of a box grater, then gather in a clean tea towel and wring as dry as possible over sink; a lot of liquid will be discarded. You want the cucumber as dry as possible. Empty cucumber shreds into mixing bowl and add yogurt, ginger, remaining lemon juice and season with salt and lots of pepper; stir together well.

Schmear the cucumber yogurt raita on a large platter. Scatter the potatoes and cooked fennel bulb on top of the yogurt. Scatter fennel rounds over the top, then sprinkle with mint leaves, fennel seeds and any reserved fennel fronds and serve immediately while potatoes and fennel are warm. Scoop up the yogurt raita with the vegetables upon serving.