Preheat oven to 350F degrees. Place a strip of aluminum foil in the bottom and up the sides of a 9x13-inch baking dish, approximately 8-inches wide by 15-inches long. This strip will help you remove your bars from the pan after freezing, as the parchment paper might rip. Line the pan with parchment paper, letting excess extend over sides of the pan. See notes for tips on the parchment paper step. Once the pan is lined, lightly rub the bottom and sides of the pan with some butter or shortening.
Next grind the pretzels for the cake base. You can do this in a food processor or with a rolling pin. In a food processor, place the pretzels in the work bowl and pulse until finely ground, about 10 times. I ground mine pretty finely but you can have some bigger pieces and it'll be great. Alternately, place the pretzels in a resealable plastic bag and crush with a rolling pin.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and 1 cup sugar, at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of the bowl. Add eggs, one at a time, beating well after each addition. Beat in 1 teaspoon vanilla.
In a medium bowl, whisk together flour, pretzels, baking powder, and salt. Gradually add the flour mixture to butter mixture alternating with the milk, beginning and ending with flour mixture, beating just until combined after each addition (in other words, add about 1/3 of the flour mixture, then half of the milk, another 1/3 of the flour, the remaining half of the milk, then the rest of the flour mixture). Spoon batter into prepared pan, smoothing the top.
Bake until a wooden pick inserted in center comes out clean, about 13 to 15 minutes. The top will turn golden and the sides will start to pull away slightly from the sides. Let cool completely in pan.