How to Make It
In a food processor, combine the first 11 ingredients and puree until blended. With the machine on, slowly drizzle in both oils. Scrape the dressing into a medium bowl and stir in the cheese and shallot. Season with salt and pepper.
In a large nonstick skillet, melt the butter in the oil. Add the panko and cook over moderately low heat, stirring, until golden, about 5 minutes. Remove the skillet from the heat. Stir in the oregano and garlic powder and season with salt. Transfer to a paper towel–lined plate to drain.
In a large bowl, toss the lettuce leaves with 1/2 cup of the dressing and season with salt and pepper. Toss to evenly coat. Layer the lettuce on plates and top with the breadcrumbs. Garnish with grated cheese and parsley and serve, passing the remaining dressing at the table.