Step 1

Fill a large pot with about 1" water; season with a big pinch of salt. Set a steamer basket in pot. Cover pot and bring water to a boil. Add potato, cover, and steam until fork-tender, 20–25 minutes.

Step 2

Meanwhile, toss sliced fennel, onion, vinegar, and ¼ tsp. salt in a medium bowl. Let sit, tossing occasionally, at least 10 minutes and up to 30.

Step 3

Heat 2 Tbsp. oil in a large skillet over medium-high. Add lamb, cumin, cinnamon, 1 tsp. pepper, and ½ tsp. salt and press into an even layer. Cook, undisturbed, until well browned on the bottom, about 4 minutes. Break up into pieces with a spatula and continue to cook, stirring occasionally, until browned, 1–2 minutes. Push mixture to one side of skillet and add mushrooms in an even layer; season with salt. Cook, undisturbed, until beginning to brown and soften, 3 minutes, then stir together with lamb mixture. Continue to cook, stirring occasionally, until mushrooms are golden brown, about 2 minutes more.

Step 4

Whisk yogurt, lemon juice, and remaining 1 Tbsp. oil and ¼ tsp. salt in a small bowl.

Step 5

Divide potato halves between bowls and mash slightly with a fork. Top with yogurt sauce and mushroom mixture. Lift fennel and onion out of vinegar with your hands and scatter over bowls; discard vinegar. Top with mint, fennel fronds (if using), and pepper.