Melt the butter.
Add the loose Chai tea to the butter and infuse for several minutes. Once infused, strain the butter through a fine colander or filter directly into the cake mix.
Combine cake mix, infused butter, and egg and mix until well blended.
Take the cookie batter, a tablespoon at a time and roll it into a ball. Roll each ball of batter in a shallow dish of powdered sugar and place onto a cookie sheet lined with parchment. Dip the bottom of a large drinking glass into the bowl of powdered sugar and press gently on the top of each cookie ball to flatten.
Bake at 350 degrees until just beginning to brown on the edges. Remove from the oven and cool on a rack.
While the cookies are baking, whip up the heavy cream along with the sugar, extract, and pinch of salt. When the cookies are cool, spread the whipped cream onto half the cookies (or use a disposable bag like a ziplock with a small cutoff corner to squeeze the filling onto the halves). Add a second cookie to make a sandwich. Roll the edges of the sandwiches in dried lavender flowers.