In a medium bowl, mix together the dicd tuna, green onions, ginger, wasabe, sesame oil, soy sauce and lime juice until tuna is well coated.
Cover with plastic wrap and store in fridge while you make the cones.
Prepare the miso cones by preheating the oven to 350ºF.
In a mixmaster, combine the sesame seeds, sugar, butter, corn syrup and flour until the butter is well incorporated.
Line a baking sheet with parchment paper and scoop small spoonfuls of the dough onto the baking sheet. Space them far apart as they will spread during baking.
Bake for 4 to 6 minutes until golden brown.
Remove from oven and roll into cone shapes.
Spoon the chilled tuna tartare into each cone and serve immediately.