Heat a large sauté pan over medium heat. Add sun-dried tomatoes and heat until oil is released. Add onions and garlic and sauté for 2 minutes. Add peppers and cook until tender, 2 to 3 minutes.
Add baby spinach, mustard, and thyme to the pan. Cook until spinach is wilted, about 3 minutes.
In a large bowl, combine oats with broth or water, egg, and baking powder. Season with salt and pepper, to taste. Fold in cooked vegetables and cheese.