Step 1: Infuse butter
In a medium pot, melt butter over medium-low heat. Remove from heat and submerge black tea bags and Chai Spices in butter. Infuse for 20 min. Strain into a medium bowl. Remove and reserve 2 Tbsp. infused butter for icing. Cool to room temperature.
Step 2: Mix dough
Preheat oven to 350 degrees. Lightly oil mini muffin tin and sprinkle with sugar to coat bottom and sides of cups. In the bowl of a stand mixer fitted with the paddle attachment, combine 1 cup granulated sugar, salt, Ground Turmeric, and infused butter. Mix on medium-high for 2 to 3 min. until fluffy. Reduce speed to medium and add eggs, egg yolk, and Madagascar Vanilla Bean Paste one at a time, mixing until smooth between each addition. Reduce speed to slowest setting and add flour, stirring until just barely combined. Remove bowl from mixer and use a rubber spatula to ensure dough is combined.
Step 3: Make icing
In a medium bowl, combine glaze ingredients and stir until smooth. Glaze should reach a consistency that will drip partway down sides of cakes. Add additional powdered sugar or milk if needed to reach this consistency. Set aside and stir occasionally until ready to use.
Step 4: Bake and ice
Fill cups of mini muffin tin with 2 Tbsp. dough and press to flatten top. Bake for 10 to 12 min. until barely golden around the edges and center is still soft. Cool for 10 min. in tin. Twist cakes to ensure they will release from tin then turn out onto cooling rack. Arrange cakes upside down on cooling rack and allow to cool completely. Top each cake with a generous 1 tsp. of icing and use bottom of teaspoon to gently encourage it to drip down sides of cakes. Allow icing to set and serve.