Prep the butter. In a medium, heavy-bottomed saucepan, melt the butter over low heat, about 10 minutes. Stir regularly to prevent the butter from getting too hot—at no point should the butter sizzle, crackle, or pop. Once the butter has melted, remove from heat and immediately whisk in the Earl Grey tea.
Prep the rest of the ingredients. In a medium bowl, whisk together the flour, baking powder, baking soda and salt. In a large bowl, combine the sugars.
Make the cookie dough. Pour the melted butter and tea over the sugars and mix with a heatproof rubber spatula until just combined. Add the egg and vanilla and mix until just combined. Gradually mix in the dry ingredients and mix until just combined. Add the chocolate all at once and mix until evenly distributed throughout. Assemble the cookies. Line a quarter sheet pan with parchment paper. Use a 3-Tablespoon cookie dough scoop to portion the cookie dough into balls, placing them next to each other on the sheet pan. Cover the pan loosely with plastic wrap and refrigerate overnight.
Prep your pans and oven. Line two half sheet pans with parchment paper. Place the chilled cookie doughs at least 3 inches apart on the prepared sheet pans. Position a rack in the center of the oven and preheat to 350°F.
Bake the cookies. Bake one pan at a time for 10 minutes, or until the edges have set but the centers are still gooey. The cookies will look puffed when you pull them out of the oven, but will fall and crack into the perfect cookies as they cool. Cool the cookies on the pan on a wire rack for 20 minutes, or until the edges and bottoms of the cookies have set and feel firm to the touch. Repeat with the remaining cookie dough.
Serve and store. Serve warm or at room temperature. The cookies can be stored in an airtight container or zip-top bag at room temperature for up to 3 days.