Combine half of the onion, the vinegar and a pinch
of salt in a medium microwave-safe bowl. Microwave
until hot; set aside.
Heat the olive oil in a large skillet over medium-
high heat. Add the remaining onion and cook,
stirring, 3 minutes. Add the artichokes and heat
through, 4 minutes. Stir in half of the spinach
and cook until wilted, 2 more minutes. Remove from
the heat and stir in the asiago, goat cheese,
mayonnaise and the remaining spinach.
Heat a grill pan over medium heat. Sandwich the
spinach-artichoke mixture between the bread
slices. Brush the sandwiches with olive oil and
add to the grill pan. Grill 3 minutes per side.
Let rest 2 minutes; cut in half.
Drain the reserved onion. Drizzle with olive oil,
then add the tomatoes, parsley, and salt and
pepper to taste; toss. Serve with the sandwiches.