8tablespoonsunsalted buttercut into chunks, plus extra for greasing the pan
For the filling
1 1/3cupsgranulated sugar
8tablespoonsbuttercut into chunks
Powdered sugarfor serving (optional)
Place a rack in the center of the oven and preheat the oven to 350 degrees. Line an 8-inch square baking dish with two 8-inch wide strips of parchment paper facing opposite directions to make a "sling". Butter the parchment paper.
Place the crust ingredients into a food processor and pulse until the mixture resembles coarse crumbs and sticks together when you press between your fingers. Scrape into the prepared pan and use your fingers or the flat bottom of a dry measuring cup to press the crust into the pan and smooth it out. Bake for 20 minutes, until lightly browned. Leave the oven on when you remove the pan.
While the crust is baking, wash the food processor. Zest the lime and place the zest into the food processor. Cut the pith (white under the lime zest) away from the lime and discard. Cut the lime flesh into thin slices and place into the food processor.
Place the cherries and the sugar into the food processor with the lime flesh and zest. Process on high until smooth, about two minutes, scraping down the sides of the bowl as needed. Add the butter and purée until smooth, scraping down the sides of the bowl.
Add the eggs, the cornstarch, and the salt to the lime-cherry mixture and pulse, scraping down the sides, until well-blended. Pour into the crust and bake for 35-40 minutes, until center jiggles just slightly when the pan is jostled. Remove from the oven and cool completely. Cut into 16 squares and sprinkle with powdered sugar before serving if desired.