Heat 1 tablespoon olive oil in a skillet over medium heat. Add the chopped onion and a pinch of salt and cook 4–5 minutes until softened and translucent. Add the minced garlic and grated carrot and cook another 2 minutes until fragrant. Remove from heat and let cool slightly.

Combine patty mixture

In a large bowl add the cooked brown rice and cooked lentils. Lightly mash with a fork or potato masher until mostly combined but still retaining some texture (about 10–15 presses). Add the rolled oats, cooled onion/carrot/garlic mixture, chopped parsley, cumin, smoked paprika, kosher salt, black pepper, and the thickened flax mixture. Stir until evenly combined. If the mixture feels too wet, add up to 2 tablespoons more oats; if too dry, add 1–2 teaspoons water.

Form patties

Divide the mixture into 4 equal portions (about 3/4 cup each). With slightly wet hands, form each portion into a compact patty about 3.5 inches (9 cm) wide and 1/2 inch (1.2 cm) thick. Press the surface firmly so the patties hold together while cooking. Chill patties in the refrigerator for 20 minutes to help them set (optional but recommended).

Cook patties

Heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium heat. Add patties (work in batches if needed) and cook 4–5 minutes per side until a golden-brown crust forms and patties are heated through. Flip gently with a spatula to avoid breaking. If desired, finish in a 350°F (175°C) oven for 5–7 minutes to ensure they're warmed through.

Burger Assembly & Toppings

Prepare sauce

In a small bowl whisk together the mayonnaise, Dijon mustard, and lemon juice. Taste and adjust seasoning with a pinch of salt if needed.

Prepare avocado

Slice the avocado and toss gently with the 1/4 teaspoon salt and a squeeze of lemon if desired to prevent browning.

Toast buns

Slice the buns and toast cut sides in a skillet or toaster until lightly golden (about 1–2 minutes) — you can brush with a little olive oil first for extra crispness. Sprinkle sesame seeds on the top buns if using.

Assemble burgers

Spread a tablespoon of the sauce on the bottom half of each toasted bun. Place a handful of mixed greens, then a cooked garden patty, two tomato slices, a few rings of red onion, and avocado slices. Top with another teaspoon of sauce on the bun top and close the burger.

Serve

Serve immediately with your choice of sides (sweet potato fries, a simple salad, or kettle chips). Leftover patties keep covered in the refrigerator for up to 3 days and reheat gently in a skillet or oven.