Prepare Rosemary Browned Butter:In a small skillet over medium-high heat, heat butter and rosemary until the butter melts and begins to foam. Continue cooking, swirling the pan occasionally, until the butter turns a golden brown and gives off a nutty aroma. Be careful not to burn the butter.Remove from the heat immediately and allow to cool slightly.Remove rosemary sprigs from butter.
Make Sweet Potato Filling:Place prepared sweet potatoes in a medium saucepan and add enough water to cover them, plus an extra inch.Bring the water to a boil and cook the cubed sweet potatoes for about 15 minutes, or until they are very tender.Drain the sweet potatoes, and place them back in the pot.Add mascarpone, salt, and 2 tablespoons of the prepared Rosemary Brown Butter. (Reserve the rest of the browned butter for the final step.)Using an immersion blender, puree ingredients until everything is smooth and creamy, with no lumps remaining. (You can do this step in a food processor if you don’t have an immersion blender.)
Fill Squash Blossoms: Place Sweet Potato mixture in a zip-top bag, trim one comer and use to pipe into each blossom. Carefully pipe the mixture into the flowers. Do not overfill the flowers.
Gently twist the petals closed at the top as shown. Spray or brush stuffed flowers very lightly with with olive oil.
Grill Stuffed Squash BlossomsPreheat grill (indoor or outdoor) to medium-high heat. Place filled squash blossoms on hot grill for 3-4 minutes.Use tongs to turn the squash blossoms over, and grill another 3-4 minutes.
Using a spoon, skim the clear browned butter from the top of what remains after making the filling. (Leave the dark brown remains at the bottom of the bowl.) Drizzle the clear browned butter over the grilled squash blossoms.I put the remaining browned butter in a small bowl for this step. Garnish with fresh rosemary sprigs and serve warm.
Alternative Prep Method: You can also bake the filled squash blossoms in a 375° F oven for 10-15 minutes.If you wish, you can use tweezers to remove the stamen from the male blossoms before you fill them.