In a 3- to 4-quart pan over high heat, bring 2 1/4 cups water, 1 tablespoon olive oil, 1/2 teaspoon salt, and cayenne to a boil. Remove from heat, add couscous and sugar snap peas, cover, and let stand until couscous is tender to bite, about 5 minutes. Fluff with a fork.
Meanwhile, place halloumi slices in a single layer in a 10- to 12-inch nonstick frying pan over medium-high heat. Cook, turning once, until browned on both sides, 5 to 7 minutes total. Remove pan from heat, but leave cheese in pan to keep warm.
In a 1-cup glass measure, mix lemon juice, remaining 1/4 cup olive oil, and salt and pepper to taste. In a large bowl, mix salad greens with 1/4 cup of the dressing. Mound equally on four plates. Stir cherry tomatoes, parsley, and mint into couscous and mound over greens. Top portions equally with halloumi slices, then dressing. Garnish with lemon wedges.