Preheat oven to 400°F.
Sprinkle the work station with flour. Unfold the puff pastry sheet onto the flour, smooth out with a couple light strokes with a rolling pin, about 12-inch square sheet. Use a round 1 ½ inch biscuit cutter or mold to cut out the pastries. Place each round onto a baking sheet covered with parchment paper and cook in oven for 15-20 minutes or until golden brown.
Meanwhile, whip the goat cheese and heavy cream. Set aside.
Chop off the florets off of the Broccolini and cut into 2 cups of small florets.
In a sauté pan over medium-high heat, warm 2 tablespoons of olive oil then add Broccolini, garlic and salt. Sauté Broccolini until just tender, about 5-6 minutes.
To assemble the tarts, slice the cooked puff pastry which will have double in height.
If the inside of the puff is not fully cooked, place back in the oven opened to the inside and bake for about 4 minutes.
Place ¼ goat cheese mixture in each bottom of the puff, place the small Broccolini floret on top of the goat cheese mixture and then place the lid on top.
Serve as an appetizer.