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1
Soak sliced onion in a bowl of ice and cold water 15 minutes, then drain well and pat dry.
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2
While onion soaks, stir together cheeses, chives, zest, and pepper in a bowl with a rubber spatula until combined well.
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3
Spread about 1 1/2 tablespoons cheese mixture evenly over each of 2 tortillas (keep remaining tortillas covered with plastic wrap). Top 1 tortilla with an even layer of salmon, covering cream cheese completely, then top with other tortilla, cheese side down. Make 5 more quesadillas in same manner, then stack on a plate and chill, covered with plastic wrap, until ready to heat.
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4
Halve, pit, and peel avocado, then cut lengthwise into 1/8-inch-thick slices. Lightly brush avocado slices with lemon juice.
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5
Heat griddle over high heat until very hot, then reduce heat to moderate. Lightly brush 2 quesadillas on both sides with some oil, then toast on griddle (1 at a time if necessary) until undersides are golden with some blackened spots, about 1 minute. Flip quesadillas over with a spatula and toast until undersides are golden with some blackened spots, 1 to 2 minutes, then transfer to a baking sheet, arranging in 1 layer, and cover with foil to keep warm. Toast remaining quesadillas in same manner, using a second baking sheet.
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6
Heat remaining oil in a 12-inch heavy skillet over high heat until hot but not smoking, then cook tomatoes, stirring occasionally and seasoning with salt and pepper, until just beginning to soften, about 1 minute.
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7
Transfer quesadillas to plates, then top with onion, avocado, tomatoes, and arugula.
