Peel, trim, and quarter carrots lengthwise, then cut crosswise into 3-inch long pieces; transfer to a plate.
Trim and halve celery lengthwise, then cut crosswise into 3-inch long pieces; add to the plate with the carrot and set aside.
Slice tomatoes crosswise into rounds.
Thinly slice mozzarella.
1 (8 oz) block mozzarella cheese
Preheat a large skillet over medium-high heat.
While the skillet heats up, place the bread slices on a flat surface. Evenly spread each slice with pesto; layer half of the slices with tomato and mozzarella. Cover sandwiches with the remaining bread slices.
8 slices whole grain bread
½ cup sun-dried tomato pesto
Once the skillet is hot, add butter and swirl to coat the bottom. Place sandwiches in the skillet and cook until the bottoms are golden brown, 2-4 minutes.
4 tsp butter, unsalted
Remove the sandwiches to a plate and add more butter to the skillet; return sandwiches to the skillet, browned-side up, and cook until golden brown on the other side and the cheese is melted, 2-4 minutes more. Once done, transfer to a cutting board and slice in half.
4 tsp butter, unsalted
Divide sandwiches and veggies between plates; serve with ranch for dipping. Enjoy!