In a medium-sized skillet, heat the olive oil over medium heat. Spread alternating layers of onions and salt, like lasagna, in the skillet. Continue this process until there are no more onions or salt. Top with the bundle of tied basil.
Stirring occasionally, cook the onions until lightly browned, about 20 minutes.
Place the bread, caramelized vegetables, chopped basil and balsamic vinaigrette into a large bowl. Toss to evenly coat. Let the salad rest for 15 minutes and then serve topped with freshly grated pecorino.
In a small bowl add the vinegar, lemon zest and juice, garlic and dijon, then whisk to combine.
Next, add the olive oil; a few drops at a time, whisking constantly.