Melt butter in a saucepan over medium heat. Reduce heat to medium-low. Add carrot, corn, green onion, and garlic. Cook and stir until fragrant but not browned, about 6 minutes. Add spinach; cook, stirring occasionally, until heated through and wilted, about 4 minutes. Remove from heat.
Stir sour cream and 8 ounces plus 2 tablespoons cream cheese into the spinach mixture. Spread mixture over the center of each tortilla. Roll the wraps together and seal with toothpicks. Place wraps on a baking sheet.
Bake in the preheated oven until golden brown, about 15 minutes.