Set the oven to broil. Drizzle the rosemary sprig with the oil and sprinkle with salt. Place it on a baking sheet and roast for one minute, or until the oil is hot and the aromatics of the rosemary have been released. Wait for the rosemary to cool, then remove the leaves and roughly chop.
Peel half of one orange and finely dice the rind. Juice both oranges and add the juice to a small saucepan. Bring to a simmer over medium-low heat. Add the diced orange rind, chopped rosemary, grated ginger, and sugar. Stir until the sugar has dissolved, then bring to a boil and remove from the heat. The liquid will have evaporated, leaving a sugary syrup behind. Leave the syrup to cool.
Pour 15 milliliters of the Rosemary and Orange Syrup into a champagne flute. Top with Prosecco and ginger beer. Lay the rosemary sprig in your palm and give it a high five to release the natural aromas. Place it in the champagne flute to garnish.