In a large, non-stick skillet over medium-high heat, melt butter and olive oil together. Add chopped shallots and sauté for 1 minute.Add broccoli, mushrooms, and garlic to skillet; sauté an additional 2 minutes.Add chicken broth; simmer for 5 minutes, or until liquid is slightly reduced.Reduce heat to medium and add 1 ½ cups of heavy cream; simmer for 5 minutes, or until sauce is thickened.Stir in remaining ½ cup of cream, Gruyere cheese, and smoked turkey; simmer for 10 minutes, stirring frequently until cheese is melted.Meanwhile, cook pasta in a large pot of boiling, salted water until tender, but still firm to bite. Drain well and add to skillet, stirring to coat evenly.Season sauce to taste with freshly ground black pepper. Stir in chives, and half of Parmesan cheese. Transfer to serving dish and top with remaining Parmesan cheese.