Bring a medium pot of water to a boil. Prepare a bowl of ice water. Blanch asparagus for 2-3 minutes, until tender-crisp, and no more. Plunge asparagus into ice water to stop the cooking so it stays crisp. Once chilled, pat to dry.
Remove crusts from bread. Overlap two slices by about half an inch and roll flat with a rolling pin.
Spread with 1 tbsp lemon chive cream cheese.
Arrange smoked salmon slices over the surface of the sandwich, making sure to cover the entire area. Place three stalks of asparagus at one short end of the bread, trimming to just fit the length of the bread.
Roll tightly into a spiral, starting with the asparagus end, so the asparagus is in the center of the roll.
Wrap roll in plastic. Repeat with remaining bread and salmon to create a second sandwich roll.
Refrigerate for at least 30 minutes so the spiral shape will set. Slice each sandwich roll into four small pinwheel tea sandwiches. Garnish with chopped chives.
Make-ahead options: You can make the lemon chive cream cheese several days in advance, and you can blanch the asparagus a day ahead. Sandwiches are best the day you make them, but you can assemble them a day ahead and slice them the day you eat them if necessary.