To get started, preheat your oven to 350°F. Next, prepare a 10-inch fluted tube pan by greasing it and sprinkling it with sugar. Now, in a food processor, combine 1/2 cup sugar, almonds, and 1 tablespoon lavender, processing until finely ground.
Start by creaming the butter and the remaining sugar in a large bowl until it's light and fluffy. Next, incorporate the almond mixture, making sure it's well combined. Then, add the eggs one at a time, ensuring you beat well after each addition. Finish by incorporating the vanilla.
In a small bowl, blend sour cream and half-and-half. In a separate bowl, combine flour, baking soda, and salt. Gradually add the dry mixture to the creamed one, alternating with the sour cream mixture, and ensure thorough mixing after each addition.
Pour the mixture into the prepared pan and bake for 55-60 minutes, or until a toothpick inserted in the center comes out clean. After baking, allow it to cool for 10 minutes before transferring it to a wire rack to cool completely.
Create the drizzle by steeping the remaining lavender in water for 5 minutes. After straining, combine the infused water with confectioners' sugar until you achieve the desired consistency. Drizzle this mixture over the cake and, if desired, add extra lavender as a garnish.