Place a large skillet with flat sides over medium-high heat and add olive oil and butter.
Stir in onions and cook for 15 minutes, stirring occasionally.
Stir in garlic, salt, and pepper; cook an additional 5 minutes or until onions have browned and are jam-like in texture.
Stir in sherry and scrape the bottom of the skillet to remove any brown bits on the bottom.
Stir in water, beef broth, thyme leaves, parsley, and Worcestershire sauce.
Add broken linguine and stir to incorporate pasta into the liquid.
Bring to a boil and boil for 10 minutes, stirring occasionally, until pasta is cooked and most of the liquid is absorbed.
Remove from heat and cover for 3 minutes.
Toss in grated Parmesan, Gruyere, and garnish with thyme sprigs and chopped parsley, if desired.