Begin by browning the butter. To brown the butter, simply take a small pan and put it over medium heat on the stove. Add the butter and whisk frequently until the butter turns an amber/honey like color with brown build up on the bottom of the pan. Remove the pan from the heat and pour the browned butter into a small heatproof bowl.
Next, stick the small bowl of browned butter into the fridge and let it sit until it has cooled (about an hour or so).
After the browned butter has cooled, add the butter and sugars to a mixing bowl. Mix the browned butter and sugars until they form a wet sand like consistency and they are uniform.
Then add the wet ingredients, the sourdough, egg, and vanilla, to the butter mixture. Mix it all together, but be careful not to overmix. Set aside.
Now, mix together the flour, baking soda, salt, and corn starch. Then add the flour mixture to the sourdough mixture slowly. Mix until everything is uniform. Next, cover the cookie dough and stick it it the fridge for at least a couple hours or overnight.
After Cooling in the Fridge...
When the cookie dough has hardened, take it out of the fridge and roll the cookie dough into ping-pong sized balls and preheat your oven to 375 degrees Fahrenheit. Pour a little sugar is a small, shallow bowl to roll the cookie dough balls in (optional). Stick the dough balls on the cookie sheet lined with parchment paper, making sure to space the dough balls out at least a few inches. And then, use your thumb to make an indentation in the center of each dough ball. Make sure that you smooth out any cracks that might form in the dough to prevent jam from spilling out of the cookies.
Soften your jam or fruit preserve in the microwave for a few seconds until it is liquid like. Spoon the jam into each of the indentations and then stick the cookies into the oven for about 10-13 minutes or until the cookies are golden around the edges. Let the cookies cool a few minuets and then transfer to a cooling rack and enjoy!