Heat two cups olive oil in a stew pot or enameled pan. Add tomatoes and garlic; heat on low until tomatoes are soft and their skins are starting to split. Remove tomatoes and garlic from oil with slotted spoon and reserve.
Slice sweet potatoes into rounds, until you have 12 rounds total; reserve remaining sweet potato, squeezing out of the skins into a mixing bowl. Mash remaining potato mixture. Add in sour cream, one tablespoon of Greek vinaigrette, and salt/pepper.
Brush sweet potato rounds with remaining two tablespoons olive oil. Add to a hot grill pan or flattop grill. Cook until browned on one side and flip, turning down the heat if necessary to ensure that potato is cooked through.
Dress kale with remaining three tablespoons of Greek vinaigrette.
Place one tablespoon of the mashed potato mixture on each of the grilled steaks or rounds. Top with two or three tomatoes/garlic, then kale. Garnish with edible petals.
Repeat until you have 12; serve immediately.