Preheat oven to 350°F (Gas Mark 4). Whisk together Chobani, eggs and ½ t salt.
Heat oil in a large, heat-safe skillet over medium-high heat. Add peppers, onions and remaining salt and cook, stirring often, until soft, about 6 minutes. Stir in garlic, thyme and black pepper and cook about 1 minute.
Pour egg mixture over vegetables and gently stir to combine. Transfer to oven and bake until eggs are puffed, golden-brown and firm to touch, about 20-25 minutes. Let rest 5-10 minutes before slicing and serving.