1. Brown the Butter: In a light-colored saucepan, melt the unsalted butter over medium heat. Continue to cook, stirring occasionally, until the butter turns a rich amber color and nutty brown bits form at the bottom. This usually takes about 5-8 minutes. Immediately pour the browned butter into a heatproof bowl to stop the cooking process and allow it to cool slightly.

2. Cream Sugars and Butter: Once the browned butter has cooled for about 10 minutes (it should still be warm but not hot), transfer it to a large mixing bowl. Add the granulated sugar and light brown sugar. Beat with an electric mixer on medium speed until light and fluffy, about 2-3 minutes. The mixture should be well combined and creamy.

3. Incorporate Wet Ingredients: Beat in the eggs one at a time, ensuring each egg is fully incorporated before adding the next. Stir in the vanilla extract and the sourdough discard until just combined. The mixture might look a little curdled at this stage, but don’t worry, it will come together.

4. Combine Dry Ingredients: In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix the dough; overmixing can lead to tough cookies.

5. Fold in Chocolate Chips and Chill: Gently fold in the chocolate chips until evenly distributed throughout the dough. Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes. Chilling is crucial for flavor development and to prevent the cookies from spreading too much. For best results, chill for 1-2 hours.

6. Shape and Bake: Preheat your oven to 375 F (190 C) and line baking sheets with parchment paper. On a lightly floured surface, roll out the chilled dough to about 1/4-inch thickness. Use a heart-shaped cookie cutter to cut out cookies and carefully place them about 2 inches apart on the prepared baking sheets.

7. Bake Until Golden: Bake for 10-12 minutes, or until the edges are lightly golden brown and the centers are still slightly soft. The cookies will continue to set as they cool.

8. Cool and Enjoy: Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. Enjoy your delicious sourdough chocolate chip heart cookies!