Place the shallot in a small bowl. Pour over the verjus, vinegar, and salt, and let macerate for 10 minutes. Whisk in the olive oil, and adjust seasoning to taste.
Place the lettuce and fennel in a bowl, season with a pinch of salt and a few cracks of black pepper. Add a few tablespoons of vinaigrette and toss the salad, being sure to coat all the leaves evenly. Taste a piece of lettuce and adjust the seasoning. Top the salad with the seasoned sunflower seeds.