Heat 2 quarts of water in a sauce pan and season it lightly with salt. Trim the milkweed shoots of their leaves up to the top of the stalk, if the top leaves are small and tender, leave them if you like. While the water is heating,
Heat a cast iron or teflon pan with the butter, when it is totally melted, but not sizzling, add the egg. Reduce the heat to low and cook until the white is set but the yolk is still creamy, about 4-5 minutes, then turn off the heat and reserve.
When it's time to serve, wait for the water to come to a rolling boil, then add the milkweed shoots and cook for 30 seconds. Remove the shoots and drain for a second on a paper towel to remove excess water that could dilute the vinaigrette.
Arrange the milkweed on a plate with the shoots all facing the same direction. Cut the egg with a ring mold if desired to remove excess white, then place on the milkweed shoots. Spoon on the vinaigrette to taste, garnish with the chive flowers and the parmesan, and serve immediately.
Duck eggs can be swapped out for chicken eggs, but they won't be as rich or large. If you're feeling abitious, try out the circular shape with the egg, just cut it with a ring mold or a glass after they've been fried, it gives them a fun look.