1 cup walnut halves
1 tablespoon walnut oil
Kosher salt
1 small shallot, minced
1/4 cup fresh lemon juice
1 tablespoon Champagne vinegar
1/2 cup extra-virgin olive oil
Freshly ground pepper
4 ounces yellow squash, thinly sliced
3 thin red onion slices, separated into rings
4 heads Little Gem lettuce
1/4 cup freshly grated Pecorino Romano cheese, plus more for serving
Preheat the oven to 350°. Toast the walnuts on a pie plate until golden, 12 minutes. Let cool, then coarsely chop the nuts. Transfer to a bowl and toss with the walnut oil and a pinch of salt. In a small bowl, combine the shallot, lemon juice and vinegar and season with salt. Let stand for 10 minutes. Slowly whisk in the olive oil and season with pepper.
In a large bowl, toss the squash with the onion, lettuce, walnuts, pecorino and half of the dressing and serve. Reserve the remaining dressing for another use.