Preheat the oven to 425ºF.

Cook the quinoa: In a fine-mesh strainer, rinse the quinoa.

In a small sauce pot, combine the quinoa, burger spice blend, and 1 cup lightly salted water and bring to a boil. Reduce to a simmer, cover, and cook until the quinoa is tender and the water is absorbed, 15 to 20 minutes. Fluff the quinoa with a fork. While the quinoa cooks, prepare the sweet potatoes.

Roast the sweet potatoes: On a sheet pan, toss the sweet potato wedges with 1 tablespoon oil and the paprika, if using, and season generously with salt and pepper. Spread in an even layer and roast, stirring once halfway through, until tender and lightly browned, 20 to 25 minutes. While the sweet potatoes roast, make the burgers.

Prep the burgers: Rinse the black beans.

Scrub or peel the carrots and trim off the ends; grate or finely chop the carrots.

Trim the root ends from the scallions; finely chop the scallions.

In a large bowl, using a fork or the bottom of a heavy cup, smash 1 cup black beans into a paste. Add the carrots, eggs, quinoa, scallions, panko, and remaining whole beans. Season generously with salt and pepper, and stir to combine. Using wet hands, form the mixture into four 1-inch-thick patties.

Cook the burgers: In a large frying pan over medium heat, warm 2 tablespoons oil until hot but not smoking. In batches if needed, add the patties and cook until a dark golden-brown crust forms, 4 to 6 minutes per side; after flipping the burgers, top each with a cheddar cheese slice. While the burgers cook, prepare the garnishes and buns.

Prep the garnishes; toast the buns. Trim the root end from the lettuce; tear the leaves into burger-size pieces. Scrape off any seeds from the roasted peppers; thinly slice the peppers.

Toast the whole wheat buns in the oven until lightly crisped, 2 to 5 minutes.

Serve: Transfer the buns, cut sides up, to individual plates. Spread each bottom bun with 1 tablespoon creamy Parmesan sauce, then top with a burger, lettuce, and roasted peppers; close the buns. Serve the sweet potato fries, remaining sauce, and ketchup and mustard, if desired, on the side.