Heat oven to 325°F. Line an 8-inch square pan with parchment, leaving overhang.
Stir crumbs, sugar, and salt in a bowl. Pour in melted butter; mix until evenly moistened.
Press mixture firmly into pan. Bake 9–11 minutes until lightly set. Cool while you prepare filling.
Beat cream cheese and sugar until smooth and fluffy, about 2 minutes.
Blend in sour cream, lemon zest, vanilla, and salt. Scrape the bowl well.
Whisk lemon juice with cornstarch until smooth. Beat into filling just to combine.
Pour filling over warm crust. Smooth the top and tap to release bubbles.
Bake 24–28 minutes, until edges are set and center jiggles slightly.
Cool completely on a rack. Chill at least 3 hours to set.
Dust with powdered sugar. Slice into bars and serve chilled.