Chill the browned butter: We want to freeze the butter until it’s solid throughout but trust me, this speeds it up: Freeze the butter in the bowl for 30 minutes then give it a full stir, scraping down the sides, mixing the still melted parts in the center over the solidified chunks. Return to the freezer for another 30 minutes — it should now be totally solid throughout. Cut it into chunks, right in the bowl. No need to make them even.
Heat your oven: To 300°F. Line an 8-inch square cake pan with parchment paper that extends up two sides. There is no need to grease it.
Make the shortbread dough one of two ways:
Both methods: Transfer shortbread dough to prepared baking pan and your fingers to press it into an even, flat layer, then use an offset spatula to smooth the top.
Bake the shortbread: For 30 minutes — it will not be fully baked yet — and remove from the oven just long enough to shape the shortbread.
To create the diamond shape shown, use the back of a paring knife (yes, the dull side) or a bench scraper to make light line indentations barely 1/4-inch into the shortbread, about 1 inch apart. Then, at about a 45-degree angle from the first lines, make remaining indentations 1.5 inches apart. [Note: I absolutely never measure and it’s more intuitive than it sounds when you read the above.] Use a very thin, sharp paring knife (this is my go-to) to cut along these lines to the bottom of the pan. Use the back of a wooden skewer (the dull end) to dock the shortbread wherever it suits you (it’s for aesthetics) about 1/3 of the way into the cookie.
Finish baking: Return the shortbread to the oven for another 15 to 20 minutes, or until more deeply golden at the edges. Let cool in the pan, or, if you’re impatient, let them cool for 10 minutes, and then remove them, using one of the extended sides of the parchment paper lining the pan to make it easier. Let shortbread cool completely, then separate the shortbread where they were cut. If needed, use your paring knife again to make clean separations.
Squiggle with icing (optional): Space shortbread evenly out on a rack and place over a tray to catch drips. Place powdered sugar in a small bowl and add 1 tablespoon lemon juice, mixing to combine. We’re looking for a thick but drizzle-able consistency. Add all or part of remaining 1/2 tablespoon lemon juice if needed to achieve it. Transfer icing to a sandwich bag and snip a tiny bit of the corner off and drizzle the icing over the shortbread. Let set for one hour at room temperature.
Do ahead: Shortbread keeps for 1 week, if not longer, at room temperature. It freezes well too, just wrap it tight, and don’t squiggle with icing until defrosted.