Preheat oven to 375°F (190°C). Line two baking sheets with parchment paper.

Lightly flour a work surface and roll out the puff pastry sheets. Cut 16 rounds using a 3" cookie cutter or similarly sized glass. 

Pierce the dough all around with a fork. Place them on the baking sheets. 

With the back of a small spoon, rub the mustard onto each round, then evenly sprinkle on the cheese, top with a tomato slice, brush with olive oil, and season with salt and pepper.

Bake until pastry is golden brown, about 30 minutes. Turn the baking sheets once during cooking to help the pastry brown evenly. 

Place the baking sheets on wire racks to cool. Garnish with chopped chives and serve.