Preheat the oven to 350 degrees F (180 degrees C). Line an 8×8-inch square pan with enough parchment paper to have overhang on all sides.
For crust, beat butter, sugar, and salt together in a large bowl with an electric mixer until light and fluffy. Add egg and vanilla and beat until thoroughly combined. Mix in pretzel crumbs. Mixture will be somewhat sticky.
Pour dough into the prepared pan and press evenly into the bottom of the pan with the back of a silicone spatula.
Bake in the preheated oven until crust begins to turn golden, 20 to 25 minutes. Remove from the oven and allow to cool while preparing filling.
For filling, add brown sugar, butter, water, corn syrup, and salt to a heavy-bottomed sauce pot over medium-low heat. Bring mixture to a boil, stirring constantly, and boil for 5 minutes. Carefully pour in cream, stirring constantly. Bring mixture back up to a boil and continue to cook for an additional 20 minutes, stirring frequently, until an instant-read thermometer reads 245 degrees F (113 degrees C). Remove pan from heat and stir in vanilla and lemon juice.
Carefully pour hot filling over crust. Place pan into the freezer until filling is cool to the touch, 30 to 40 minutes.
For topping, place chocolate chips, cream, and corn syrup into a microwave-safe bowl. Microwave on 50% power in 30 second intervals, stirring after each interval, until mixture is melted and combined. Pour chocolate over the top of the chilled filling, and spread into an even layer. Gently press extra pretzels into the chocolate, if desired. Refrigerate bars until chocolate has firmed up, about 1 hour.
Remove bars from the pan using the parchment overhang. Carefully peel off parchment paper. Run a knife under hot water and wipe dry with a towel. Cut into 16 bars using the hot knife, wiping the blade clean after each cut.