For the burgers: Add flax and 3 Tbsp. water to a small bowl. Mix and set aside to gel, about 10 minutes.
Meanwhile, add onion and garlic to a small saucepan with a drizzle of olive oil. Season with salt and pepper, and sauté until translucent, 3-5 minutes. Transfer to a large bowl.
Add chickpeas to a food processor, and pulse until broken into small pieces. It should look like rice/riced cauliflower. Add it the same large bowl.
Add cashews to the food processor, and pulse until broken into small pieces. Add it to the large bowl same bowl.
Add Italian Seasoning, basil, olive oil, balsamic, a healthy dose of salt and pepper, and the flax-water mixture, and mix to combine. Add oat flour and mix until combined. The mixture will be slightly tacky, but easily shaped into a patty with wet hands. If it’s too wet, add more oat flour 1 Tbsp. at a time. Shape into 7-8 patties, wetting your hands slightly between forming each patty.
Heat a skillet over medium heat. Add a drizzle of olive oil, and cook each patty until browned. Flip, and cook until browned.
For the caramelized onion: Add sliced onion and olive oil to a small skillet. Heat over medium-low heat until dark and caramelized, 10-15 minutes. Stir only occasionally.
To assemble: Spread hummus on both the top and bottom buns. Top with a patty, caramelized onion, and basil. Devour.