Preheat the oven to 350 degrees F (175 degrees C). Line a large-rimmed baking sheet with parchment paper. Add crackers in one even layer.
Add butter, 1/3 cup plus 2 tablespoons brown sugar, vanilla extract, and 1/2 teaspoon cinnamon to a saucepan over medium-high heat; cook, stirring often, until well combined and simmering, 2 to 4 minutes. Remove from heat.
Carefully pour butter mixture over the layer of crackers. Using a silicone spatula, toss crackers until well coated in butter mixture.
Bake in the preheated oven until bubbling and golden brown, about 10 minutes, flipping and tossing crackers halfway through cooking time.
Meanwhile, stir granulated sugar and remaining 3/4 teaspoon cinnamon together in a small bowl.
Remove crackers from the oven and allow to cool, 1 to 2 minutes. Transfer to a large bowl and toss with cinnamon sugar mixture until well coated. Transfer to a serving bowl.
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