Melt the butter in a cast-iron or other heavy skillet over medium heat. Dump in the onion slices and sprinkle them with a pinch of salt. Cook, stirring frequently, for 8 to 10 minutes or until the onion slices are soft and tender, then pour in the wine, cognac, and beef broth. Cook for 20 to 25 minutes, stirring frequently, until the liquid has mostly cooked off and the onions are very soft and deep amber in color. Stir in the sugar and season with salt as needed.
Preheat the oven to 500°F. If using a baking stone/steel, place the stone/steel in the bottom third of the oven before you start preheating.
Stretch or roll out your dough to a 12- to 14-inch circle, then transfer it to an oiled or parchment-lined baking sheet or a lightly floured pizza peel (if using a baking stone/steel).
Drizzle the dough with a little olive oil and sprinkle it with salt. Transfer to the oven and bake for about 5 minutes, just until the crust turns golden. Remove the parbaked crust from the oven.
If you're using a baking stone or steel, switch your oven setting to Broil on high, and let it heat up for 5 to 10 minutes.
Spoon the caramelized onions onto the parbaked crust, spreading them out evenly. Make sure you get as much of the gooey sauce as possible—it will really bring forward the French-onion-soup flavor. Sprinkle the cheeses over the onions.
Transfer the topped crust to the oven and bake until the crust is deep golden brown and the cheese is bubbly and charred in spots, about 5 minutes on a baking stone or steel, 5 to 7 minutes on a baking sheet.
Remove the pizza from the oven and let it cool for at least 5 minutes before slicing.