Preheat the oven – Preheat the oven to 350°F (177°C) and line a baking sheet with parchment paper.
Cream the butter and oil – Add the softened salted butter and vegetable oil to a mixing bowl. Beat with a hand mixer or stand mixer until light and fluffy.
Add the sugar and wet ingredients – Add the granulated sugar, powdered sugar, egg, and vanilla extract. Mix until smooth and evenly combined.
Add the dry ingredients and chai – Add the flour, baking soda, kosher salt, and loose tea from the opened chai tea bag. Mix just until the dough comes together and no dry streaks of flour remain.
Chill the dough – Cover the cookie dough and refrigerate for 1 hour. Chilling helps the cookies hold their shape and bake up thick and chewy.
Shape the cookies – Divide the chilled dough into 12 evenly sized balls. Roll each ball in granulated sugar, arrange on the prepared baking sheet, and gently flatten each one.
Bake the cookies – Bake at 350°F (177°C) for 9–14 minutes. For a soft, chewy texture, remove the cookies while they are still slightly underbaked in the center rather than waiting for them to become deeply golden.
Cool completely – Allow the cookies to cool before glazing so the glaze stays on top instead of melting into the warm cookies.
Make the chai glaze – Whisk together the sifted powdered sugar, cinnamon, nutmeg, 2 tablespoons of milk, and loose chai tea until smooth. Add additional milk as needed until the glaze reaches a smooth consistency for spooning over the cookies.
Glaze the cookies – Spoon the chai glaze over the completely cooled cookies. Sprinkle lightly with cinnamon, if desired, and allow the glaze to set before serving.