Melt butter in a small sauce pan (make sure you use one with a cover!) Add onions and stir to coat in the butter. Cook, covered for 30 - 45 minutes, stirring occasionally.
Remove onions from heat and set aside.
Heat over to 425° and line a sheet pan with parchment paper. Unroll the puff pastry sheet onto the sheet pan and use a pizza cutter to cut the sheet into 9 squares.
Bake until golden brown, 10 - 12 minutes.
Break open the puff squares to create two equal shells. Sprinkle some of the onions over each shell, spread the fig jam, and top with the goat cheese.
Put back in the oven for 4 -6 minutes, or until cheese begins to brown.