Heat a skillet over medium heat; add oil. Add onion; cook and stir until onion has softened and turned translucent, about 5 minutes. Reduce heat to low and continue cooking and stirring until onion is very tender and dark brown, about 40 minutes more. Remove from heat and cool.

While the onion is cooling, cut the figs lengthwise into 1/4-inch rounds.

Layer 1/4 teaspoon goat cheese, 1/4 teaspoon caramelized onions, and 1 or 2 fig slices on each cracker.