In the bowl of your stand mixer, place the butter and the sugar. Using the paddle attachment, beat together well for 3-4 minutes. If you don't have a stand mixer, you can just use a hand held mixer.
Add the egg and vanilla and beat well until incorporated, about 1 minute.
Add the lavender, salt and baking powder, and mix briefly. Add one cup of flour and mix 20-30 seconds , then add the second cup and mix just until all the flour is incorporated.
Remove the dough from the mixer and shape into a disc. Wrap tightly with plastic wrap and store in the refrigerator for at least an hour or two, but ideally overnight.
Preheat oven to 350 degrees.
Remove from the fridge and cut in half. Flour your work surface and the top of the dough, and then roll it out to about 1/8" to 1/4" thickness.
Using a cookie cutter, cut rounds of the dough out and place them on a baking sheet. They cookies will not spread much, so they only need about 1" of space between them. Now, using a smaller round cutter, cut out the middles of half of the cookies.
Bake in preheated 350 degree oven for about 9-10 minutes until they are dull. You don't want them to be golden, just maybe a little on the edges. Remove from oven, and once cool enough to handle, remove to a wire rack to cool completely.
Microwave your jam for about 30 seconds, just to make it more easily spreadable. Lay your rounds out on your work surface, and top each one with a dollop of jam, using the back of the spoon to spread it out. Top each one with a cookie with a hole.
Sift icing sugar over top of all the cookies.
Store in an airtight container for up to a week, or in the freezer for up to a month.