Preheat oven to 400°. Mix garlic, coriander, cumin, and oil in a large bowl. Add cauliflower and chickpeas; season with salt and pepper. Toss to coat.
Transfer cauliflower mixture to a parchment-lined rimmed baking sheet. Wipeout bowl; reserve. Bake, tossing halfway through, until chickpeas and cauliflower are golden brown and cauliflower is tender, 18–22 minutes.
Meanwhile, mix yogurt, a quarter of the lemon juice, and a big pinch of salt in a small bowl.
Toss fennel, serrano chili, parsley, sesame seeds, and remaining lemon juice in reserved bowl.
Spread yogurt mixture in serving bowls. Top with spiced chickpea mixture. Scatter fennel salad over, then drizzle with oil.