Melt the butter in a large, wide skillet over medium heat. Add the sliced onions and 2 pinches of salt, and stir until the onion slices are coated in the melted butter.
Cook, stirring every 5 to 7 minutes, until the onions are very soft and turn amber in color. First, they will look like they are burning a little (they're not!), then they will begin to turn golden, and eventually, after 30 to 40 minutes, that color will deepen to brownish orange (amber). If the onions look dry after 15 or 20 minutes of cooking, of if they actually start to char at the edges, reduce the heat to low and continue cooking, stirring every 5 minutes or so, until they reach that amber color.
Pour the broth into the skillet, and scrape the bottom of the pan to release all the stuck-on brown bits. Cook for 1 to 3 minutes, until the broth has reduced and the onions look saucy, not soupy. Remove the skillet from the heat, and let the onions cool before using them as a pizza topping.
When the onions have cooled to around room temperature, spoon them onto a round of pizza dough (you'll need about ½ cup per 12- to 14-inch pizza). Top with any cheese and other toppings you like, then bake and enjoy!