Preheat oven to 425 degrees F (220 degrees C). Line a baking sheet with aluminum foil.
Heat olive oil and 1/2 teaspoon sesame oil in a skillet over medium-high heat; cook and stir tofu, working in batches, until lightly browned on 1 side, 2 to 3 minutes. Flip using chopsticks and cook until lightly browned on the other side, 2 to 3 minutes.
Whisk water, soy sauce, brown sugar, cornstarch, ancho chile pepper, and garlic together in a bowl, adding more water if sauce gets clumpy.
Mix tofu, cabbage, carrot, cucumber, cilantro, and green onions together in a bowl; mix in sauce until coated. Spoon mixture down the center of each egg roll wrapper; roll wrapper around the filling. Apply water to the edges of the wrapper so it sticks together. Arrange egg rolls on the prepared baking sheet and spray with cooking spray.
Bake in the preheated oven, flipping halfway through, until golden brown, 20 to 30 minutes.