Combine coconut, pistachios and almonds in a small bowl.
Whisk together sweetened condensed milk, cardamom, vanilla extract and salt in a separate bowl; set aside.
Melt coconut oil in a medium, heavy-duty pan set over low heat. Add chickpea flour; stir to combine. Cook, stirring frequently, for 10 minutes or until the mixture is toasted and aromatic.
Whisk in the sweetened condensed milk mixture until the chickpea flour is completely incorporated and mixture is thick and smooth. Remove from heat; add powdered sugar, stirring until all lumps are dissolved. Add half the nut mixture; stir to combine.
Transfer the mixture to prepared dish; spread the burfi evenly with a spatula. Sprinkle with remaining nut mixture and press lightly into the top.
Refrigerate for 2 to 3 hours; cut into bars and serve. Store in an airtight container for up to 7 days.