In a food processor, blend the goat cheese, buttermilk, 2 Tbs. of the olive oil, mayonnaise, and lemon juice until smooth. Transfer to a medium bowl and stir in the chives. Season to taste with salt and pepper.
Put the arugula in a large bowl. Using a mandoline set at a very thin setting or a vegetable peeler, shave the fennel and add to the arugula. Toss with enough of the dressing to just coat the salad. Season to taste with salt and pepper. Divide the salad among 4 large salad plates and mound slightly. Toss the tomatoes in a bowl with the remaining 1 tsp. olive oil and a little salt and pepper; scatter on the salads. Serve immediately, passing the remaining dressing at the table.
nutrition information (per serving):
Photo: Scott Phillips