In bowl of standing mixer fitted with flat beater, mix flour, sugar, figs, and salt on low speed until combined, about 5 seconds. With mixer running on low, add butter 1 piece at a time; continue to mix until mixture looks crumbly and slightly wet, about 1 minute longer. Add vanilla and cream cheese and mix on low until dough just begins to form large clumps, about 30 seconds.
Press dough in even layer into parchment-lined 17 1/2 by 12-inch baking sheet. Bake cookies on lower-middle rack in 375-degree oven until golden brown, about 20 minutes.
Immediately after removing baking sheet from oven, sprinkle evenly with chocolate chips; let stand to melt, about 3 minutes.
Using offset icing spatula, spread chocolate into even layer, then sprinkle evenly with chopped hazelnuts. Cool on wire rack until just warm, 15 to 20 minutes.
Using pizza wheel, cut into 1 1/2-inch diamonds. Transfer cookies to wire rack to cool completely.