Heat butter over medium high heat in a large pot or dutch oven.
Just before the melted butter begins to brown, add 1-2 tsp of the fresh thyme [or 1 tsp thyme] and cook for 30 seconds longer.
Add sliced onions and stir to coat.
Turn heat down to medium, and stir onions until cooked completely, about 20-30 minutes
About 5 minutes before the onions are done, throw in 2-3 cloves of super thinly sliced garlic.
When onions are a gently caramelized golden brown and the bottom of the pan is beginning to go brown, throw in .5 c of white wine to deglaze [stock also works], scraping brown bits up into a bubbly light brown sauce.
Add stock and water and bring to a boil.
Turn the heat down to a low simmer.
Add herbs, salt, and cognac.
Cook for 15 minutes.
Place soup in a bowl and top with a few thin slices of piave vecchio or alternative.
Allow cheese to melt from the heat of the soup and serve immediately.
Add pepper to taste at the table.
Serve with slices of toasted seedy brown bread, slathered with mustard, if you dare!