In a frying pan, cook finely diced onion with 2 tsp. canola oil until softened; let cool completely. Meanwhile, slit shishito peppers* lengthwise on one side to within 3/4 in. of each end.
Mix onion, ground chicken or turkey breast, lightly beaten egg, minced shiso leaves*, and kosher salt and pepper. Stuff peppers with filling.
Heat a grill to medium (400° to 450°) with a perforated grill pan on cooking grate. Mix soy sauce and 1 tbsp. canola oil. Brush all over peppers, then tip them into hot grill pan.
Brown on each side, 4 to 6 minutes total. Transfer to a platter, drizzle with a little soy, and scatter bonito flakes on top if you like.
MAKE AHEAD Through stuffing of peppers, chilled airtight, up to 1 day.
*If you don’t grow shishito peppers and shiso, find them at farmers’ markets and (along with bonito flakes) at Asian grocery stores.