Three things go into making this recipe really smooth: creamy peanut butter, like Jif or Skippy (our test-kitchen's go-to for baking); and room-temperature eggs and cream cheese.
Preheat oven to 350 degrees. Brush a 9-by-13-inch baking dish with butter.
Finely grind crackers in a food processor. Add melted butter, peanuts, brown sugar, and 1/2 teaspoon salt; pulse until peanuts are chopped and texture of mixture resembles wet sand.Transfer to prepared baking dish; press firmly and evenly into bottom and three-quarters of the way up sides. Bake until set and slightly darkened, 12 to 15 minutes. Let cool completely.
Reduce oven to 325 degrees. In a mixer fitted with the paddle attachment, beat cream cheese and peanut butter on medium speed until smooth. Gradually beat in granulated sugar until lightand fluffy, scraping down sides of bowl as needed. Beat in remaining 1/2 teaspoon salt. Beat in eggs, one at a time, then vanilla until smooth. Pour filling into cooked crust; smooth top with asmall offset spatula. Bake until puffed and set along edges but still slightly wobbly in center, 40 to 45 minutes. Let cool completely.
Whisk jelly in a saucepan over medium until melted. Pour evenly over cake, then tilt dish to spread jelly to edges in a thin, even layer. Refrigerate until jelly is firmly set, about 4 hours.Cut cake into squares, wiping knife between cuts for clean edges, or cover and refrigerate up to 3 days.