2 tablespoons unsalted butter
1 tablespoon olive oil
1 bunch green onions, white portions only, finely chopped
1 cup chopped yellow onions
1/4 teaspoon salt, plus more to taste
1/4 teaspoon freshly ground white pepper
1 teaspoon chopped fresh thyme leaves
3/4 cup Roasted Garlic
1/4 cup dry white wine
2 quarts chicken or vegetable stock (or canned low-sodium chicken or vegetable broth)
3 to 4 (2-by-3-inch) Parmigiano-Reggiano rinds (optional)
1/2 cup heavy cream
1/2 cup cubed rustic Italian bread, plus more if desired
2 tablespoons chopped fresh parsley
1 tablespoon fresh lemon juice
Chopped chives, garnish