Preheat a grill to medium and lightly grease the grates with canola oil.
Drizzle the red pepper, jalapeno and sliced onions with olive oil, and season them with salt, pepper, to taste, and curry powder. Grill the vegetables over medium heat until they have grill marks and are softened, approximately 5 minutes. Allow them to cool, then peel off the skin of the red pepper. Finely chop the onions and pepper and set aside. Reserve the jalapeno for the aioli.
In a small saute pan over medium heat, add the 2 tablespoons olive oil, 1/4 cup curry powder, the grated garlic, grated ginger, turmeric, coriander, cumin, and garam masala, if using. Allow the spices to toast in the oil until fragrant and become slightly darker in color, approximately 2 to 3 minutes (If this mixture seems dry, feel free to add a little more oil to the pan.) Allow the spices to cool slightly.
In a medium-sized bowl, use a fork or chopsticks to combine the beef, the spice mixture, the grilled red pepper, red onion, green onions, ketchup, brown sugar and soy sauce. Season with salt and black pepper, to taste. Cover the mixture with plastic wrap and refrigerate for at least 1 hour (Marinating overnight is even better to help the flavors marry.)
Remove the burger mixture from the refrigerator, and divide it into 4 equal-sized quadrants. Brush the patties with olive oil, season both sides with salt and pepper, and put them the grill. Cook the patties to medium-rare or medium doneness, about 3 minutes on the first side, then 4 to 5 minutes on the second side. Make sure to rotate the patties once on each side to achieve nice crosshatch marks. Once cooked, transfer the patties to a plate and tent them with aluminum foil. Allow them to rest for at least 10 minutes.
Combine the mayonnaise, mint, green onion, grilled jalapeno, garlic, curry powder, cumin, lime zest and juice in a food processor. Pulse until the mixture is well integrated, but there are still chunks of green onion and jalapeno remaining. Season the puree with salt and black pepper, to taste. Set aside.
In a small bowl, toss together the fried onions with the garam masala until they are evenly dusted with the spice. Set aside.
While the burgers rest, halve the brioche rolls, and put them, cut side down, on the grill grates. Toast until they are a light golden brown, about 10 seconds. Set aside.
To serve, generously spread 1 tablespoon of aioli onto each side of the rolls. Press 4 to 5 slices of cucumber into the mayonnaise on the bottom of the roll. Top the cucumbers with a handful of baby lettuce, then a burger patty, and finally, approximately 1/4 cup of the fried onion mixture. Cover with the top of the buns and serve immediately with a side salad and the Grilled Sweet Potato Fries.
Add the egg yolk, salt, dry mustard, and sugar to a large bowl. Whisk by hand or with an electric mixer until combined. Pour in the lemon juice and vinegar and whisk once more.
While whisking continuously, very slowly drizzle in the canola oil. Keep drizzling until the mixture has emulsified and the entire cup of oil has been incorporated into the egg mixture. Refrigerate in an airtight container for up to 2 weeks.
I use Malaysian curry powder from my father's pantry, but any good quality curry is fine. Make sure that you adjust the amount depending on the heat of your curry powder.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.