Preheat oven to 375°. Cook pork over medium-high heat until no longer pink, breaking up with a spoon. Drain off fat.
Add onions, garlic, and carrot. Cook over medium heat until the onions are soft.
In a small bowl, whisk together soy sauce, cornstarch, water, and sesame oil. Pour over cooked mixture, stirring to mix. Let cool slightly.
Place egg roll wrapper on work surface and brush with water.
Spoon about 3 tablespoons of filling on bottom third of wrapper, leaving a 1/2" border on the bottom and sides.
Pull bottom edge over the filling and roll up, pinching ends to seal.
Place seam side down on parchment-lined baking sheet. Brush with vegetable oil. Bake at 375° for 20 minutes, or until golden and crisp. Serve with siracha sauce or Chinese mustard.