Heat a large skillet or wok over medium heat. Add the 1-tablespoon of oil and swirl to coat the pan. When the oil shimmers, add the onions and saute, stirring occasionally, until soft and browned, 6 to 8 minutes. Mix in the thyme, sage, and rosemary and season with salt and pepper, to taste. Add the mirin, and cook to evaporate the liquid, about 6 minutes. Cool.
Arrange a sheet of the nori, shiny side down, on a rolling mat. Have a small bowl of water handy. Place a salmon fillet on the bottom half of the nori sheet and season with salt and pepper. Arrange 1/4 of the onions on the upper 1/3 of the salmon. Roll, wet the edge, and press the mat to seal. Repeat with the remaining nori, salmon, and onions. Allow the maki to rest, seam side down, for 2 minutes.
Fill a fryer or heavy medium pot 1/3 full with the oil and heat over high heat to 425 degrees F. Place the flour in a medium bowl and slowly whisk in the club soda until the mixture resembles a light pancake batter. Dip the rolls in the batter and fry all at once, turning as necessary, until golden, 4 to 6 minutes. Remove the rolls with a mesh spoon and drain on paper towels. Season, to taste, with the salt and pepper.
With a sharp knife, slice each maki in half. Cut one piece straight across into 3 pieces and cut the other piece diagonally into 2 pieces. Serve with dipping sauce.
Wasabi Soy-Honey Dipping Sauce:
In a medium bowl, combine the soy sauce, vinegar, wasabi, honey, and sesame oil. Stir to blend.