Preheat oven to 400 degrees. HINT: For extra crispy fries, place the baking sheet in the oven while it's preheating! Peel the sweet-potato and cut into 1/2-inch matchsticks (like French fries!). On a baking sheet with 1 tablespoon olive oil and season with salt and pepper. Place in the oven and roast for 20 minutes, tossing half way through, until golden brown and crispy.

Meanwhile, core and seed 1 tomato, then finely chop. Thinly slice the other tomato widthwise. Halve, peel, and thinly slice the red onion. Drizzle the Portobellos with 1 tablespoon olive oil, season with salt and pepper. Place cap side-up on the baking sheet with the potatoes and roast for 10-12 minutes, until tender. (Keep and eye on them, they'll be done before the potatoes!)

Meanwhile, make the tomato-onion jam: heat 1 tablespoon olive oil in a medium pan over medium heat. Add the onion and chopped tomato and cook, stirring often, until jammy, 10-15 minutes. Add a splash of water if the jam becomes too thick. Season with salt and pepper.

While the jam cooks, separate the head of butter lettuce leaves. Slice the brioche buns in half horizontally. Top with the mozzarella cheese, then place in the oven for about 5 minutes, until the cheese is melted.

Make the basil aïoli: chiffonade the basil by stacking the basil leaves on top of each other, then roll them into a cigar, and thinly slice into ribbons. In a small bowl, combine the basil, mayonnaise, and a pinch of salt and pepper.

Assemble the burgers: spread each brioche bun with the basil aïoli and top with a Portobello mushroom, a few tomato slices, tomato-onion jam, and lettuce. Serve with the sweet potato fries to the side. Enjoy!