Melt 3 sticks unsalted butter in a large, light-colored skillet or small pot over medium heat. Continue to cook, stirring occasionally, until the milk solids have separated from the fat and turn dark golden brown and smell nutty, 8 to 10 minutes.

Carefully scrape the browned butter into the bowl of a stand mixer (or large heatproof bowl if using an electric hand mixer). Refrigerate until firm and cold to the touch, about 1 ½ hours.

Meanwhile, line an 8x8-inch baking pan with 2 sheets of parchment paper, positioning them perpendicular to each other so that the parchment hangs about 2 inches over all 4 sides of the pan to form a sling.

Add ⅔ cup granulated sugar and 1 teaspoon kosher salt to the brown butter. Beat with the paddle attachment on medium-low speed until light and fluffy, about 1 minute. Scrape down the sides of the bowl with a flexible spatula.

Add 3 ⅓ cups all-purpose flour and beat on the lowest speed until a dough just comes together, about 1 ½ minutes.

Transfer ¾ of the dough (23 ounces or 2 ⅔ cups) to the baking pan. Press into an even layer with your hands or the bottom of a measuring cup. Dock the dough by pricking all over with a fork.

Spread ¾ cup jam evenly over the top. Crumble the remaining dough in small pieces and scatter evenly over the jam, covering most of the jam. Freeze while the oven heats.

Arrange a rack in the middle of the oven and heat the oven to 350ºF. Bake until lightly browned on top, 45 to 55 minutes.

Sprinkle with ¼ teaspoon flaky salt. Immediately run a thin knife or offset spatula along the edges of the shortbread to loosen from the parchment.

Let cool completely in the pan, 1 to 1 ½ hours. Grasping the excess parchment paper, lift the shortbread slab out of the pan and place on a cutting board. Discard the parchment paper. Cut into 16 (4x1-inch) pieces.