Add the cranberries, orange juice, brown sugar, cinnamon, and a pinch of salt to a sauce pot. Simmer the berries until jammy, stirring occasionally, about 15-20 minutes. Let cool.
Preheat oven to 350 degrees. Grease 2 9-inch or 3 6-inch cake pans generously with butter.
In a large bowl, beat together the sugar, butter, and Greek yogurt until light and fluffy, about 2-3 minutes. Beat in the eggs, one at a time, until fully incorporated. Beat in the vanilla. The batter may curdle a bit from the yogurt. Add the flour, baking powder, baking soda, and salt. With the mixer running, stream in the champagne and mix until just combined. The batter will froth and take on a puffy texture. This is normal! Swirl in the cranberry jam with a spatula. Do not overmix - you want swirls in the batter.
Divide the batter amongst the cake pans. Bake for 35-45 minutes until the center no longer jiggles and an inserted toothpick emerges clean. Cool 10 minutes in the pans, then run a knife around the edges and invert onto a wire rack. Cool completely.
To make the buttercream: beat together the powdered sugar, butter, vanilla, and 1/4 cup heavy cream. If needed, add 1-2 tablespoons more cream to create a "whipped" texture.
Lay one layer of cake on a cake stand or plate. Pipe a 1/2-1 inch barrier around the circumference (see photos for reference). Spread the remaining cranberry jam in the middle of the frosting fence. Set the second cake layer on top. Frost the cake generously. Adorn with fresh cranberries and flowers, as desired.