Step 1Chop the cilantro, jalapeno and garlic and place in a medium bowl. Add the lime juice, white wine vinegar and mayonnaise. Place the mixture in a blender and blend until smooth. This makes about 2 cups jalapeno-cilantro mayonnaise. It can be kept in the refrigerator, covered, for up to 5 days.
Step 2Double-fry the sweet potato slices: Add vegetable oil to a large pot, enough to come 2 to 3 inches up the sides of the pot. Heat the oil to 300 degrees, and blanch the sweet potato slices in the oil for 4 minutes, then cool on a rack. Increase the oil to 350 degrees, then fry the slices again for 1 minute.
Step 3Butter the brioche slices and toast. Spread the jalapeno mayonnaise on one side of two slices of brioche. Divide the turkey and place on top of the two slices. Add the fried sweet potato discs and sliced avocado and cilantro sprigs and spread more of the jalapeno-cilantro mayonnaise on top. Invert the remaining slices of brioche onto the sandwiches. Serve immediately.