Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a fluted tube pan (such as Bundt®).

Bring water to a boil in a saucepan. Steep tea bags in the water for 5 minutes. Squeeze tea bags over the saucepan and discard. Bring tea to a boil.

Combine butter and chocolate in a large mixing bowl. Pour in the hot tea; whisk until melted. Beat in sugar and egg yolks using an electric mixer.

Mix sour cream and baking soda together in a separate bowl. Add to the batter, mixing well. Mix in flour and baking powder.

Beat egg whites in a glass or metal bowl until stiff peaks form. Fold into the batter. Pour batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 40 minutes. Cool in the pan for 10 minutes, then invert onto a plate. Let cool completely, about 30 minutes.

Make glaze while the cake is cooling. Melt chocolate chips and butter together in a small saucepan over low heat. Stir in half-and-half until blended. Remove from heat; stir in confectioners' sugar and peppermint extract. Drizzle over cooled cake.