Place a large skillet over medium-high heat with 2 turns of the pan of vegetable oil, about 2 tablespoons. While the oil is heating up, grab a large mixing bowl and add the ground ginger, the red curry paste, lime zest and juice, honey, garlic, salt and freshly ground black pepper.
Use your hands to mix everything up then press the meat down into the bottom of the bowl. Use the side of your hand to score the meat into four portions. Scoop out one portion and shape the rest of the meat and same way to make four burgers.
Once the oil in the pan is hot, lay the burgers in and cook them, turning once, until golden brown on the outside and cooked through, about 6 minutes per side.
While the burgers are cooking, get our your blender or food processor and combine the shallots, hot sauce, tamari, peanut butter, remaining grated ginger and an extra-large splash of water (about 1/2 cup). Turn the machine on puree everything to make a dipping sauce (if you need it a little thinner, add a little more water- remember you can alwas add more but you can't take it out!). Transfer the sauce to one large or four individual serving dishes and set aside.
When the burgers are about done, prepare four plates or a platter with a small stack of lettuce leaves for each burger. Lay the burger down over the leaves and top each with some of the sliced pepper, cucumber and chopped basil. Serve the burgers up with the dipping sauce alongside and a knife and fork.