Line a rimmed baking sheet with aluminum foil. Set aside.
Place butter under skin of chicken, dividing evenly. Pour olive oil over skin, dividing evenly. Sprinkle chicken evenly with garlic salt and pepper, rubbing some underneath skin.
Roast until chicken is done and skin is golden brown, 30 to 35 minutes. (Chicken meat should be white and opaque when done with no pink juices.) Let chicken rest for 15 minutes before slicing.
When ready to slice for sandwiches, remove skin and discard. Remove breast meat from bone in one piece. With a sharp slicing knife, cut breast meat into thin slices approximately 3x1¾ inches. Wrap well in aluminum foil to prevent drying out. Set aside.
Using a serrated bread knife in a gentle sawing motion, trim and discard crusts from all sides of bread slices. Cut each slice into 2 (3x1¾-inch) rectangles.
Spread Tarragon-Watercress Aïoli in an even layer onto each bread rectangle. Using 12 bread rectangles (aïoli side up) as a base, assemble sandwiches by stacking ingredients in the following order: watercress, roast chicken slices, and tomato slices. Top sandwiches with remaining bread rectangles (aïoli side down).
Garnish with watercress just before serving, if desired.
Notes
*Campari tomatoes are a small, sweet variety that are the perfect size for tea sandwiches.