How to Make It
Heat oven to 350 degrees. Grease a 9 x 12 baking pan and set aside. Cut open the tea bags and empty the contents into a small bowl. Pour in enough boiling water to cover the tea by ½ inch; steep, 10 minutes. Stir together the flour and baking powder in another small bowl.
Meanwhile, melt butter in a small saucepan over low heat. Pour the melted butter into a large bowl, then stir in the sugar, eggs, yogurt, 1 teaspoon rose water, and the reserved tea and steeping liquid. Gradually add the flour mixture, stirring until just incorporated. Transfer the batter to the prepared pan.
Bake until fragrant and a toothpick inserted in the center of the cake comes out clean, 30 to 35 minutes. Transfer to a wire rack to cool completely.
To make glaze, combine confectioner's sugar, lemon juice, 1 tablespoon rose water, food coloring, and 2 tablespoons water in a small bowl. When the cake is cool, pour the glaze over the top. Set aside to firm up, 15 minutes, before slicing and serving.