Start by preheating the oven to 350°F. Next, prepare a 10-inch fluted tube pan by greasing it and sprinkling it with sugar. Set this aside for now. In a food processor, combine 1/2 cup of sugar, almonds, and 1 tablespoon of lavender. Process until you have a finely ground mixture.
In a spacious bowl, whip the butter with the remaining sugar until it's light and fluffy. Gradually incorporate the almond mixture into it. Next, add the eggs one at a time, ensuring thorough beating with each addition. Finally, blend in the vanilla.
Combine sour cream and half-and-half in a small bowl. Then, blend the flour, baking soda, and salt into the creamed mixture, adding each alternately. Be sure to beat the mixture thoroughly after each addition.
Pour the mixture into the prepared pan and bake it for 55-60 minutes. Check for doneness by inserting a toothpick into the center; it should come out clean. Afterward, let it cool for 10 minutes before transferring it to a wire rack for complete cooling.
Create a lavender drizzle by mixing water and the remaining lavender in a small bowl. Steep this mixture for 5 minutes, then strain to remove the lavender. In another small bowl, combine confectioners' sugar with the infused water until you achieve the desired consistency. Finally, drizzle this mixture over the cake, and for an extra touch, garnish with additional lavender if you like.