Preheat the oven to 350°F. Line a standard 9 × 5-inch loaf pan with parchment paper, leaving enough overhang along the sides to lift out the loaf.
Stir together the ground flaxseed and water in a small bowl. Set aside for 5-10 minutes, or until thickened.
Heat the olive oil in a medium skillet over medium heat. Add the onion and cook for 3-4 minutes, stirring occasionally.
Add the garlic and cook for about 30 seconds, until fragrant. Stir in the celery and carrots and cook for another 5-7 minutes, or until tender. Remove from the heat.
Place the chickpeas and lentils in a large bowl. Mash them with a potato masher or fork until mostly broken down, leaving a few small pieces for texture.
Add the cooked vegetables, thickened flax mixture, quick oats, nutritional yeast, garlic powder, cumin, Italian seasoning, salt, and pepper. Stir thoroughly until the mixture is evenly combined and holds together when pressed.
Transfer the mixture to the prepared loaf pan. Press it down very firmly and smooth the top, making sure there are no large gaps.
Whisk together the ketchup, soy sauce, balsamic vinegar, and maple syrup in a small bowl. Use a spoon to spread the glaze evenly over the loaf.
Bake for 45-50 minutes, or until the loaf is firm around the edges and the glaze has thickened.
Let the loaf rest in the pan for at least 20 minutes. Use the parchment overhang to lift it out, then slice carefully with a sharp knife.