In medium saucepan saute tomatoes in a tablespoon of oil and add garlic. Saute 1 minute, add remaining oil, and simmer 20 minutes to infuse flavors. Can be refrigerated and stored for future use, up to 20 days.
In a large saute pan heat butter and brown slightly over medium heat. Add shallots until they sweat: do not cook too quickly. Deglaze with brandy, reduce, then add cream and salt and pepper. Add oysters until membranes start to ruffle. Remove oysters and reserve on plate. Reduce sauce for 1 minute longer to thicken.
In another large saute pan add 1 tablespoon Tomato/Garlic Oil and when hot quickly toss arugula until wilted. On a sheet tray, place bottom shells of oysters and add arugula to each as bottom layer. Top with one oyster each and add asiago cheese to top. Flash under the broiler until cheese is golden. Remove carefully and place on a tray with rock salt as under liner. Garnish with chopped chives.