Place bulgur in a large, heatproof bowl and cover with boiling water.
Set aside for 15 minutes, drain excess water, and set bulgur aside.
Preheat oven to 400°F.
Heat oil over medium heat in a large sauté pan.
Add onions and cook until translucent, about 2 to 3 minutes.
Add garlic and cook until fragrant, 30 seconds to 1 minute.
Increase heat to medium-high and add zucchini, squash, and peppers.
Cook, stirring often, about 3 to 4 minutes.
Stir in sausage crumbles and cook until heated through, about 3 minutes more.
Add bulgur to pan, stirring to combine. Season with salt and pepper.
Pour mixture into a 9×9 baking dish, packing firmly with a spatula.
Spread mashed potatoes over mixture, then top with cheddar.
Bake 10 to 12 minutes, or until cheese is bubbling and light brown at the edges.
Let cool 3 to 4 minutes, then cut into squares and serve hot.