Heat a few inches of vegetable oil in a pot over medium-high heat. Combine 1 1/2 cups buttermilk and 1/2 cup sour cream in a bowl and add the onion rings; soak for a few minutes. On a plate, toss the flour with the chives; season generously with salt and pepper. Double-dip the onion rings in the liquid and the flour. Fry a few rings at a time in the hot oil, turning once, until deep golden, about 4 minutes. Transfer to a rack to cool.
Combine the beef, worcestershire, lots of pepper and a little salt. Form 4 large or 12 slider-size patties and coat with EVOO. Heat a large skillet or griddle over medium-high heat, add the burgers and cook, turning once, for 8 to 10 minutes for big burgers, 4 to 6 minutes for sliders.
While the burgers cook, make the dressing. In a small bowl, combine 1/2 cup each buttermilk and sour cream, the ketchup, garlic, herbs and lemon juice; season with salt, pepper and hot sauce to taste. Layer the rolls with the burgers, ranch dressing, lettuce and onion rings.