In a large saucepan, melt butter to which a few drops of oil have been added. Add scallions, garlic, and Brussels sprouts and cook over low heat for 10 to 15 minutes.
Meanwhile, separate shredded prosciutto into strands. In a skillet, sauté them in a small quantity of oil over medium-high heat until beginning to brown. Remove and drain on paper towels.
Add just enough stock to c