Cook quinoa. Pour the broth into a small pot, place it over high heat, and bring to a boil. Add the quinoa, reduce the heat to low, cover and simmer until all of the liquid has been absorbed, about 15 minutes. Set aside.
Blend remaining ingredients. Add the basil, sun-dried tomatoes, sun-dried tomato oil, almonds, bread crumbs, onion, Parmesan, garlic, egg and salt, to a food processor fitted with the blade attachment. Blend until it's a fairly smooth consistency. Use a rubber spatula to transfer this to a large mixing bowl.
Combine everything together. Add the cooked quinoa to the bowl and mix until it's evenly incorporated into the sun-dried tomato mixture. Season to taste with freshly ground black pepper. (Here's How to Season to Taste.) Shape. Cover a baking sheet with parchment paper, and then about ⅓ cup each, shape the quinoa mixture into 6 "burgers." (If you have an ice cream scoop about the right size, it's the easiest way to shape them.) Gently use the palm of your hand to press each one into a nice round shape. Set aside.
Sauté. Generously coat the bottom of a large sauté pan with olive oil and place it over medium-high heat. Once the pan is very hot, use a flat-bottomed, metal spatula to place the burgers into the pan, with a couple of inches between them. (Depending on the size of your pan, you may need to do this in two batches.) You should hear a sizzling sound — if you don’t, the pan isn't hot enough. (In order for them to crisp nicely, wait for the sizzle.) Sauté for about 2 minutes, then carefully flip the burgers over and reduce the heat to medium-low, and sauté for another few minutes or so, until the bottom is golden brown and they hold together well. Place the cooked burgers on a plate and cover with foil until you're ready to serve.