Step 1

Pick fronds from fennel stalks to equal 1/4 cup; finely chop fronds, and set aside. Remove stalks from bulb, and cut stalks crosswise into 1/8-inch-thick rounds to equal 1/2 cup; set aside. Quarter fennel bulb lengthwise through core; set aside.

Step 2

Stir together fennel fronds, yogurt, cucumber, ginger, shallot, 1 tablespoon lemon juice, 1/2 teaspoon salt, and 1/8 teaspoon pepper in a medium bowl. Chill until ready to serve.

Step 3

Meanwhile, preheat a grill to medium-high (about 450°F). Place potatoes in a microwavable bowl; cover and microwave at high until potatoes are about halfway cooked, about 5 minutes. (A fork should meet with some resistance when inserted into a potato.)

Step 4

Place potatoes on oiled grates, and grill, uncovered, turning often, until cooked through and charred, 6 to 8 minutes. Transfer potatoes to a bowl, and cover with aluminum foil to keep warm.

Step 5

Toss fennel bulb quarters with oil, and sprinkle with 1/4 teaspoon salt and remaining 1/8 teaspoon black pepper. Place on oiled grates, and grill, uncovered, turning often, until cooked through and charred on all sides, about 10 minutes. Transfer to a cutting board, and cut into 1/2-inch wedges.

Step 6

Spoon yogurt mixture onto a rimmed platter, and top with fennel wedges. Halve potatoes, arrange over fennel, and sprinkle with remaining 1/4 teaspoon salt. Toss together fennel stalk slices with remaining 1 tablespoon lemon juice in a small bowl; scatter over potatoes. Tear mint leaves, and scatter over platter; sprinkle with fennel pollen.