Add oil in a steady stream and whisk while pouring into the other ingredients.
Prepare the Salad
Combine watermelon and greens in a large bowl; add all but 1/4 cup vinaigrette, tossing gently to coat.
Transfer watermelon mixture to a serving platter, and sprinkle evenly with pecans and cheese. Season to taste with additional salt.
Pass additional dressing on the side.
Notes
There is a good assortment of Red Pepper Jellies available; mine was from Harry and David but still the same basic ingredients, red bell peppers and jalapeno, as others available at grocery stores.The Harry and David product was jammy and had chunks of both peppers in it so I had to put everything into the blender to get it smooth but I've had jelly before too and then blending it would not have been required.