Position your oven rack in the upper third and preheat your broiler to high. Line a rimmed baking sheet with foil for easy cleanup.
In a large bowl, toss the chicken pieces with 1 tablespoon olive oil, cumin, paprika, cayenne, and ⅛ teaspoon salt. Spread them evenly on your prepared baking sheet.
Broil for 5-7 minutes until the chicken is just cooked through. You’re looking for lightly charred edges and an internal temperature of 165°F.
Meanwhile, mash garlic with the remaining ⅛ teaspoon salt into a paste using a fork. Whisk in lemon juice and the remaining 2 tablespoons of olive oil.
Add the cooked chicken to the dressing and let it stand for 5 minutes, stirring occasionally to coat.
To serve, spread ½ cup hummus onto the bottom of each shallow bowl. Top with chicken, cucumber slices, cherry tomatoes, red onions, and parsley. Drizzle any leftover dressing over the bowls.