Preheat the oven to 350°F.
To make the crust, start by placing the pecans into the bowl of a food processor fitted with an s-blade. Run the machine on high-speed until the nuts are finely ground.
Place all of the remaining crust ingredients into the food processor bowl. Pulse the machine until they're well combined and form a dough, scraping down the sides of the bowl as needed.
Press the dough into the bottom and up the sides of a 9 ½ inch tart pan with a removable bottom.
Bake the crust for about 20 minutes, until lightly browned.
Place the crust on a cooling rack when it comes out of the oven.
To make the filling, place all filling ingredients into a high-powered blender or the bowl of a food processor fitted with an s-blade. Blend until smooth, stopping to scrape down the sides of the bowl or pitcher as needed.
Once the crust has cooled down a bit (it doesn't need to be completely cool — just warm is fine), pour the filling into the crust, smoothing out the top as best you can.
Chill the tart until at least partially set, about 2 hours (Note 1).
Once the filling has partially set, make the topping. Place the chocolate chips and butter into a microwave-safe bowl. Zap the mixture in 20-second increments, stirring well in between, until the ingredients are fully melted and well blended.
Dip the bottom half of each fig into the chocolate mixture, then arrange the figs on top of the tart, gently pressing them into the filling. Sprinkle the chocolate-dipped figs with the chopped pecans.
Place the tart back into the fridge until the chocolate and filling have fully set.
Slice and serve.