Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Spread tortilla wedges onto the prepared baking sheet.
Mix 1 tablespoon white sugar and cinnamon together in a small bowl. Drizzle melted butter evenly over tortilla wedges; sprinkle with cinnamon-sugar mixture.
Bake in the preheated oven until chips are crisp, about 15 minutes.
Mix cream cheese, brown sugar, 1/2 cup white sugar, and vanilla extract together with an electric mixer until smooth; fold in toffee bits. Chill brickle dip until serving time. Serve warm chips with brickle dip.