Preheat oven to 400° F.
Spray loaf pan with olive oil cooking spray and set aside. For the oil-free option, line loaf pan with parchment paper.
Whisk ground flaxseed and water together with a fork and set aside.
Heat olive oil over medium heat in a large skillet. Add chopped carrot, celery and onion and season with ¼ teaspoon salt. Cook on medium for 5-7 minutes until onion is translucent and vegetables begin to soften. For the oil-free option, add veggies and wine or broth and cook over medium heat until onion is translucent and vegetables begin to soften (this method may take a few extra minutes). Turn off heat and let stand for 1-2 minutes.
Add chickpeas, thyme, sage, white pepper, *½ teaspoon salt and the chopped veggie mixture to a food processor. Process on low or pulse until everything is well combined but not pureed, scraping down the sides as needed.
Transfer chickpea mixture to a mixing bowl. Use a spoon to stir in flax eggs, vegetable broth, gluten-free bread crumbs and chickpea flour.
Form the mixture into a loaf shape and press evenly into greased or parchment-lined loaf pan. Bake for 45-50 minutes.
Allow to cool for at least 10-15 minutes before serving. Best enjoyed topped with gluten-free, vegan gravy.