Preheat oven to 350°F.
In a small bowl, set out 1 cup peanut oil along with a small pastry brush. On a baking sheet, set out 12 paper cones.
Trim 12 wonton wrappers according to diagram (see below). Generously brush both sides of each wrapper with peanut oil. Wrap 1 wrapper around each cone and press seam together. Twist the bottom around itself and pinch to seal. Bake for 5 - 7 minutes, or until golden brown and crispy. When cones cool, twist them off the cups. Reserve.
In a medium bowl, combine tuna, peach, green onion, mint, zest and sesame seeds. Reserve.
In a small bowl, combine wasabi, sesame oil, soy, honey, ginger and lime juice. Taste and adjust if necessary. Reserve.
In a mini food processor, or in a bowl with a whisk, puree avocado and lemon juice until it is super smooth. Season to taste with salt, pepper and cayenne. Transfer to a small piping bag or a small resealable bag with the corner clipped. Reserve.