Steep the tea leaves in 3 cups cold water for 30 minutes. Strain and discard the leaves.
In a medium skillet, arrange the chicken breasts in a single layer; pour in the strained tea. Add the ginger, garlic and a pinch each of salt and pepper. Bring to a boil, then lower the heat, cover and simmer until the chicken is cooked through, 10 to 15 minutes. Remove from the heat and let stand for 15 minutes. Drain and set the chicken aside.
Shred the chicken into small pieces and place in a shallow bowl; cover and refrigerate until chilled, about 20 minutes. Stir in the mayonnaise, sesame oil, tarragon and basil until combined.
Spread each bread slice with butter and top 6 of the slices with 1/2 cup chicken salad; top with the remaining bread. Trim the crusts and cut the sandwiches into 4 triangles. Pour sesame seeds onto a saucer and dip 2 sides of each sandwich into the seeds to coat.