In the bowl of a stand mixer fitted with the paddle attachment, cream together butter, dark brown sugar and white sugar on medium speed. Stop once the mixture is smooth and lighter in color (about 5 minutes).

Add the vanilla extract and mix for an additional minute. Add the flour and salt and mix on low until well incorporated. Finish by mixing in the lemon zest. Do this on the lowest speed or by hand with a spatula.

Lay a big piece of plastic wrap out on a work surface. Transfer dough from the mixer to the plastic wrap. Roll dough into a log, wrap in plastic and place in the refrigerator. Let chill while preparing the ice cream.

In a medium, heavy bottomed saucepan, combine milk, cream and loose earl grey tea leaves. Bring mixture to just below a simmer over medium-low heat (you want to see steam rising from the surface, but minimal to no bubbles). Remove the saucepan from the heat and let steep, uncovered for 15 minutes.

While you are waiting, whisk the egg yolks and sugar in a bowl until slightly thickened.

Prepare an ice bath in a large bowl (ice and water). Set a medium sized bowl in the ice bath and have a strainer ready.

Rewarm the cream-milk mixture over medium-low heat. Once you see steam rising from the surface, slowly, while whisking, add the warm cream-milk mixture to the yolk mixture. Take your time here so you don’t scramble the yolks. Return everything to the saucepan.

Put the saucepan over medium heat and cook, stirring constantly with a wooden spoon. You will know the custard is thick enough when you see steam rise from the surface and the custard coats the spoon. Pour the custard through the mesh basket strainer into the bowl sitting in the ice bath and stir until cool.

Refrigerate until thoroughly chilled (at least 4 hours). Freeze custard in an ice cream maker according to the manufacturer’s instructions. While the ice cream is churning, take your cookie dough from refrigerator and cut into bite sized chunks. When you remove the soft ice cream from the machine, mix in the lemon cookie dough chunks. You will most likely have more dough than needed, so add as much as you like (I added a little over half of the chunks). Be sure to save those extra bites for late night snacking! Finish by freezing the ice cream until hard or enjoy soft immediately.