Pulse lavender in a food processor until finely ground. Sift to remove large pieces.

Reserve half of the lavender for the frosting.

Mix remaining lavender with granulated sugar and set aside.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Grind Earl Grey tea finely and sift out large bits.

In a bowl, whisk flour, baking powder, baking soda, salt, and ground tea.

Cream butter and sugar on high speed for 1–2 minutes until light and fluffy.

Add egg and vanilla; mix until pale and airy.

Mix in dry ingredients just until combined.

Scoop dough (2 tablespoons each), roll into balls, and coat in lavender sugar.

Place dough balls 2 inches apart and gently flatten.

Bake 6–8 cookies at a time for 9–10 minutes.

Cool on the pan for 5 minutes, then transfer to a rack.

Beat butter and cream cheese until fluffy, about 3–4 minutes.

Add powdered sugar, reserved lavender, and vanilla. Beat until smooth.

Add food coloring if desired.

Frost completely cooled cookies with about 1 tablespoon frosting each.