Melt butter in 12-inch skillet over medium-high heat. Cook, swirling skillet constantly, until milk solids in butter are color of milk chocolate and have toasty aroma, 3 to 5 minutes. Remove skillet from heat and transfer browned butter to bowl of stand mixer. Let cool in refrigerator until opaque in color and completely cool, about 30 minutes. While butter chills, adjust oven rack to middle position and heat oven to 325 degrees.

Whisk flour, salt, baking soda, and baking powder together in medium bowl. In stand mixer fitted with paddle, beat cooled butter, sugar, and milk powder on medium-high speed until light and fluffy, about 3 minutes. Add vanilla and water and continue mixing until fully combined, scraping down bowl as needed with silicone spatula. With mixer running at low speed, gradually beat in flour mixture until combined. Give dough final stir with spatula to ensure that no flour pockets remain.

Transfer dough to counter and divide into 2 equal pieces. Place 1 piece of dough (keep remaining piece covered with plastic wrap) in center of large sheet of parchment and press into approximate 4-inch square. Place second large sheet of parchment over dough and roll dough into 10-inch square, about ¼ inch thick. Remove top piece of parchment.

Using pizza cutter or chef’s knife, trim away outer ½ inch of dough to make clean square shape with neat edges. Cut dough in 3 equal strips lengthwise (about 3 inches each), then cut into 9 equal strips crosswise (about 1 inch each). Slide sheet of parchment onto rimless baking sheet (leaving cookies touching). Repeat with remaining dough.

Bake cookies, 1 sheet at a time, until edges are just golden, 16 to 18 minutes, rotating sheet halfway through baking.

Let cookies cool for 10 minutes. Cut shortbread at scored marks to separate, then let cool completely, about 30 minutes. Serve. (Cookies can be stored at room temperature for up to 10 days.)