Prepare Beet Garnish ahead of time; remove from oven and set aside. Preheat oven to 350 degrees F. Lightly grease four 8-ounce individual baking dishes with butter (ovenproof ramekins or cocotte dishes work well). Combine flour, baking powder, baking soda, salt, and spices in a large mixing bowl. Mix molasses, eggs, buttermilk, oil, and brown sugar together in a separate bowl. Add buttermilk mixture to flour mixture; whisk to combine. Fold in the beets.

Set baking dishes on a roasting tray. Divide batter among dishes and bake in the preheated oven for 20 to 25 minutes, until the cakes are puffed and a cake tester inserted in centers comes out clean.

Make Sweet Greek Yogurt by combining yogurt, honey, and vanilla in a bowl. Swirl with a wooden spoon so ingredients are just combined. Serve yogurt with warm cakes. Top each cake with Beet Garnish.

Preheat oven to 150 degrees F. Shave 1 small beet into thin slices using a mandoline or sharp knife. Line a roasting tray with parchment paper and set the beet slices out in a single layer on the pan. Cover with another sheet of parchment paper, carefully pressing out any air bubbles. Top with another tray to add weight. Bake in the preheated oven for 2 to 3 hours to dehydrate the beet slices without overcooking them.