Preheat oven to 325 degrees F (165 degrees C). Line a muffin tin with 10 paper liners.
Melt butter and chocolate in the top of a double boiler over simmering water until smooth, stirring frequently and scraping down the sides with a rubber spatula to avoid scorching, 5 to 10 minutes.
Open tea bags and pour the chai mixture into a spice grinder; grind into a fine powder, 5 to 10 seconds.
Mix flour, sugar, and chai powder together in a large bowl; add eggs, one at a time, whisking until batter is smooth after each addition. Stir in vanilla extract.
Pour chocolate mixture into batter, stirring until just combined.
Pour batter into the prepared muffin cups.
Bake in the preheated oven until a toothpick inserted in the center of a muffin comes out clean and the tops are glossy and slightly cracked, about 25 minutes.
Remove muffins immediately from tin and cool on a wire rack.
