Preheat the oven to 400 degrees F.
Slice 1/4 inch off the top of both heads of garlic. Drizzle lightly with 2 teaspoons of the olive oil, season with salt and pepper, and wrap in heavy-duty foil. Add to a sheet tray. Add the fingerling potatoes to the same sheet tray and drizzle with the remaining oil, giving a toss, and seasoning with salt and pepper. Roast both the potatoes and the garlic until the potatoes are crisp on the outside and cooked through and the garlic is fragrant, 45 minutes.
Open the packets of garlic and cool. When potatoes are cool enough to handle, slice in half lengthwise.
To make the dressing, pour in the buttermilk, sour cream, squeeze the garlic out of its skin into the bowl of a food processor, and add a pinch each of salt and pepper. Blend until smooth.
Add the radishes, arugula, romaine, potatoes and cheese to a salad bowl. Drizzle the salad with enough dressing to coat and toss all together.