1. Preheat oven to 170°.
2. Carefully shuck oysters over a small, heavy saucepan. Sever oyster meat from shells; remove oysters from shells into a fine-mesh sieve set over pan, capturing oyster liquor in pan. Place oysters in a small bowl; chill. Discard top halves of shells. Scrape adductor muscle from bottom halves of shells; discard muscle. Scrub bottom halves of shells clean. Arrange bottom halves of shells on a jelly-roll pan; place in oven.
3. Add wine and next 4 ingredients (through tarragon) to saucepan with oyster liquor, and cook over medium heat for 9 minutes or until reduced to 3 tablespoons. Strain through a fine sieve lined with cheesecloth, and discard solids. Whisk crème fraîche into liquid. Keep warm.
4. Place panko in a shallow dish. Heat a small nonstick skillet over medium-high heat. Add 1 tablespoon oil to pan, and swirl to coat. Dredge 9 oysters in panko; shake off excess. Arrange coated oysters in a single layer in pan; sauté 2 minutes on each side or until golden. Remove oysters from pan, and place 1 cooked oyster in each of 9 warm shells. Keep warm. Repeat the procedure with remaining 1 tablespoon oil, 9 oysters, panko, and shells. Top each oyster with 1 1/2 teaspoons sauce and 1/8 teaspoon caviar. Sprinkle with thyme leaves; serve immediately.