Melt 1/2 cup + 1 tbsp of unsalted butter and set it aside to cool slightly.
Add 2/3 cup + 2 tbsp of granulated sugar, 2 room temperature eggs and 1 egg yolk to a large bowl. Beat the eggs and sugar on high with an electric mixer for 5-8 minutes, or until the mixture is pale yellow and shiny. This step helps to ensure the tops of the madeleines dome properly.
Next add in 1 tsp of vanilla and 1 1/2 tsp of lavender paste and mix just until combined.
Cut open 3 Earl Grey tea bags and add the tea leaves to a food processor. Grind the tea to ensure no large leaves are left.
In a small bowl sift together 1 cup + 2 tbsp of all purpose flour, 3/4 tsp of baking powder, 1/4 tsp of salt and the tea leaves.
Slowly add the dry ingredients to the egg/sugar mixture and fold in until everything is combined.
Next pour in the cooled but still liquid butter and 2 tbsp heavy cream and fold in just until combined. Don't over mix the batter.
Cover the bowl with plastic wrap and chill in the fridge for 1 hour.
Preheat the oven to 350 degrees. Transfer the batter to a piping bag. Brush melted butter into each madeleine mold. Pipe about 1- 1 1/2 tbsp of batter into each mold.
Bake the madeleines for 12-14 minutes until they have domed.
Remove them from the oven and let them cool in their pan for a few minutes, then transfer them to a cooling rack to completely cool.