Make The Ginger Tea Base: Use the back of a teaspoon to peel the ginger then finely chop it. Place chopped ginger in a mini food processor and pulse until it's pulverized. Meanwhile, using a vegetable peeler, remove the lime peel in strips, making sure to avoid the white pith. Juice all the limes (you should have about 1 cup of juice).Bring the 4 cups of water to a simmer in a medium saucepan over medium heat. Add the ginger, lime peels, and basil and set aside off the heat to steep for 10 minutes or until the tea is as ginger-y as you'd like.
Make The Mezcal Hot Toddy Cocktails: Place 1 ounce of mezcal and 1 teaspoon of honey in the bottom of four mugs. Divide the ginger tea (with the ginger, lime peels, and basil) among the four mugs. Stir to combine and reserved lime juice or more mezcal or honey as desired to make it as sweet or boozy as you'd like.