Place Sweet Potato mixture in a zip-top bag, trim one comer and use to pipe into each blossom. Pipe the mixture into the flowers. Be careful to not overfill the flowers - there needs to be enough room at the top to twist the petals closed.
Spray or brush stuffed flowers very lightly with with olive oil.
Place on hot grill for about four minutes on each side.**
(I put the remaining browned butter in a small bowl for this step.) Using a spoon, skim the clear browned butter from the top, leaving the dark brown remains at the bottom of the bowl, and drizzle over the grilled squash blossoms.
Garnish with fresh rosemary sprigs and serve warm.