On a stovetop in a Dutch oven or its equivalent, cook the onions, thyme, bay leaf and salt in the unsalted butter over moderate heat uncovered.
Stir often until onions are very soft and translucent, about 30-40 minutes.
Add flour and cook, stirring for about one minute until the flour is incorporated.
Pour in the wine and cook, stirring until the onions absorb the liquid, about 2 minutes.
Stir in the beef broth, water and pepper. Simmer, uncovered, stirring occasionaly, for about 30 minutes.
While the soup is simmering, place the oven rack in the middle position and preheat the oven to 350 degrees Fahrenheit.
Slice the baguette into 1 inch slices. Slice the clove of garlic in half and rub garlic on each slice. Then chop into large cubes. Place on a parchment or tin foil lined baking. Drizzle with olive oil and toast for 10-15 minutes in the oven (toss once halfway through the baking time). Remove when croutons are dry and slightly brown.
Preheat oven to broil. Place soup crocks on the same lined baking sheet (having removed the croutons).
Once the soup has finished simmering, remove the bay leaf and thyme, and discard. Divide the soup into the soup crocks, then place 5-7 croutons (depending upon the size) on top of of the crocks filled with soup. Place 2 slices of Gruyère, Comte or Emmental on top of each crock (letting the cheese go over the sides). Then sprinkle with 1-2 teaspoons of Parmigiano-Reggiano.
Broil for only 1-3 minutes (no longer or the bread and cheese will burn rather than brown). Remove when cheese is melted and bubbly.
Note: In my pictures, I first did not dice the baguette slices and found it hard to eat with just a spoon as the bread needed to be cut. Upon enjoying the soup on the second day, I decided to dice the slices as shared in the instructions and found it much easier to eat as the bread was already bite size.
Note: The soup can be made at least three days in advance, refrigerated and then brought back to temperature on the stovetop when you are ready to serve. The croutons as well can be made ahead of time.