Add tea to a small bowl or cup and pour ¼ cup boiling water over it. Allow it to steep for 5 minutes.
Melt butter in the microwave (15 to 30 seconds) and allow it to cool down but not solidify.
Brush Madeleine mold with melted butter and set it aside until needed.
In a large bowl, vigorously whisk eggs, sugar, orange zest, almond extract, and salt for a minute or two until light and fluffy.
Add 2 teaspoons of tea and 1 tablespoon of the tea leaves to the batter. Mix to combine.
Chop and stir dried cherries into all-purpose flour. Mix gently into the bowl ingredients.
Use a rubber spatula to gently fold the melted and cooled butter into the batter.
Scoop 1 heaping tablespoon of batter into each buttered Madeleine mold. Rest the batter for 10 minutes then bake for 10 minutes. Rotate the pan, front to back, halfway through.
Remove the pan from the oven when the cookies have set and are golden around the edges. Immediately invert the pan onto a wire rack. Cool the cookies completely.
Add chocolate chips to a small deep bowl and melt in the microwave, stirring every 30 seconds, until the chips are completely melted. Dip the Madeleines into the melted chocolate.
Carefully rest the cookies on a wire rack and chill them in the refrigerator for about 15 minutes to set the chocolate. Bring to room temperature before serving.