Brown butter Heat a small pot over medium heat. Add butter to the pan and stir frequently as it starts to melt and bubble. Look for little brown specks to start to appear and the color to change from yellow to a light amber, 3 to 5 minutes. Once it’s lightly browned, remove from the heat and transfer to a heatproof container to cool for at least 5 minutes.
Mix wet ingredients In a mixing bowl, add in cooled brown butter, granulated sugar, brown sugar, vanilla, and an egg. Vigorously mix together with a whisk until everything is smooth (like the texture of icing).
Mix dry ingredients In a spice grinder or food processor, grind dried strawberries until it's a powder consistency. In a large mixing bowl, measure 6 tablespoons of strawberry powder along with flour, baking powder, baking soda, kosher salt, and oolong tea. Add the bowl of wet ingredients (if the sugar and butter mixture has thickened, just give it a little mix until smooth) into the bowl of dry ingredients. With a spatula, give it a loose mix until roughly combined (it's okay if it's shaggy). Add in marshmallows and give it another stir until the marshmallows are mixed in.
Make cookies Preheat an oven to 375°F, then line a metal baking sheet with parchment paper. Scoop ¼ cup of cookie dough and make it into a flat, hockey puck shape with your hands and place it onto a sheet pan. Leave a few inches of space between each puck of dough. Sprinkle cookie dough with flaky salt, then bake in the oven for 12 minutes until they've spread slightly and the tops are crackly and marshmallows melty. Cool cookies for 15 minutes until they've hardened and the bottoms are crusty. Serve with some milk and enjoy :)