Combine the flour, 1 teaspoon salt, yeast and oil in the bowl of an electric mixer. Stir in 1 cup water.
Mix on medium speed until dough comes together, about 2 minutes. Cover bowl loosely with a towel and let rest 5 minutes.
Switch to the dough hook and knead dough for 1 minute – the dough should be fairly sticky but stretchy.
Transfer dough to an oiled bowl, cover and let rise until doubled in bulk. It can take anywhere from 2 -4 hours depending on the temperature of the room. Alternatively, cover the bowl and place in the refrigerator overnight. Next morning, let the dough come to room temperature and let rise until doubled in bulk.
Make the topping
Heat the oil in a large nonstick skillet over medium-high heat. Add the onions, sugar and salt. Stir, then lower heat and cover the pan.
Cook 15 minutes or until the onions are very soft. Uncover and continue cooking until the onions are deep brown, stirring frequently, about 15-20 more minutes. Stir in the balsamic vinegar and set aside.
Preheat oven to 450 (225 C) degrees.
Place the dough on an oiled 13 x 9-inch rimmed baking pan and spread the dough toward the edges of the pan – it will spring back and not quite reach. Cover and let rest 20 minutes.
Gently dimple the dough while stretching with your fingers to evenly cover the pan the rest of the way. Bake 10 minutes.
Distribute the onions over the top of the focaccia and bake another 10 minutes.
Sprinkle the cheese, greens and walnuts over the onions and return to the oven; bake an additional 5 minutes to slightly melt the cheese and wilt the greens.
Cut into serving pieces with a sharp knife or pizza cutter. Serve warm or at room temperature.
For this recipe I used Petite Tango, a curly, spicy heirloom lettuce. If you can't find it, use leaves from a head of chicory, escarole or radicchio