Line an 8-inch square pan with parchment, letting the paper overhang for easy lifting.
Warm the condensed milk, butter, and cookie butter in a medium saucepan over low heat, stirring until smooth.
Remove from heat and stir in the white chocolate chips until completely melted and glossy.
Stir in vanilla, salt, and cinnamon until evenly combined.
Fold in half of the crushed cookies to add crunch throughout the fudge.
Spread the mixture into the prepared pan and smooth the top with a spatula.
Drizzle warmed cookie butter over the surface, swirl with a knife, and sprinkle on remaining cookie crumbs. Tap the pan to settle.
Chill until firm, about 2 to 3 hours. Lift out, cut into 16 squares, and serve.