Cranberry Chess Pie

1 (9") store-bought or homemade prebaked pie crust
12 oz. fresh or frozen cranberries
1½ cups sugar
¾ tsp. kosher salt
1 Tbsp. finely grated lemon zest (from 1 lemon)
1 Tbsp. plus 1½ tsp. fine-ground cornmeal
1 Tbsp. all-purpose flour
4 large eggs, room temperature
½ cup heavy cream
4 Tbsp. unsalted butter, melted, slightly cooled
1 tsp. vanilla extract
¼ cup fresh lemon juice
Powdered sugar (for serving; optional)

Place a rack in middle of oven; preheat to 325°F. Place pie crust on a rimmed baking sheet. Cook cranberries in a medium saucepan over medium heat, shaking pan occasionally, until some have begun to split and burst, 6–8 minutes. Drain off any excess liquid. Remove from heat and let cool (if you’re in a rush, transferring to a baking sheet or medium bowl will help them cool faster).
Combine sugar and salt in a large bowl, then add lemon zest. Use your fingers to rub zest into sugar until moist and fragrant. Whisk in cornmeal and flour, then add eggs and vigorously whisk until well combined, about 30 seconds, Whisk in cream, butter, and vanilla, then add lemon juice and whisk again. Set a few cranberries aside for the top. Gently fold in remaining cranberries with a rubber spatula, breaking up any clumps.
Gently pour mixture into pie crust and dot reserved cranberries over top of custard (this makes for the most photo-worthy dessert). Bake pie until top is golden brown and set but custard still jiggles in the center (about a 3" radius), 60–70 minutes. If your pie isn’t as brown as you’d like it, you can increase oven temperature to 350°F for the last 5–10 minutes. Transfer pie to a wire rack and let cool (custard will fall as it cools). Transfer pie to the fridge and chill at least 1 hour.
Just before serving, dust with powdered sugar if using. For the cleanest slices, cut with a hot dry knife (just like if you were cutting cheesecake).