Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper or a silicone baking mat.
In a large mixing bowl, combine the unsalted butter, vegetable oil, and granulated sugar. Using a hand mixer or stand mixer, cream the ingredients together until the mixture becomes smooth and light in texture.
Add the egg, vanilla extract, and chai tea leaves to the bowl. Continue mixing until the ingredients are fully incorporated and the mixture appears evenly blended.
In a separate bowl, sift together the all-purpose flour, baking soda, salt, cinnamon, and nutmeg. Gradually add the dry ingredients to the wet mixture, stirring gently until a cohesive dough forms. Avoid overmixing, as this may affect the final texture of the cookies.
Cover the dough and refrigerate for approximately 1 hour. Chilling the dough helps the cookies maintain their shape during baking and allows the spices to develop deeper flavor.