Heat broiler. Split zucchini lengthwise; scoop out and discard seeds. Place on a foil-lined rimmed baking sheet, and toss with oil and 1/4 tsp each salt and pepper. Broil cut side down for 4 minutes. Flip zucchini and leave on baking sheet.Advertisement
Meanwhile, bring a medium pot of water to a boil, add potatoes and cook 8 to 10 minutes, until tender. Drain and transfer to a large bowl. Smash potatoes with yogurt and half the cheddar. Stir in corn, chicken, thyme and 1/4 tsp each salt and pepper.
Divide potato mixture evenly among zucchini. Top with remaining cheddar. Broil 8 to 10 minutes, until browned and heated through.