1. Make the Pheasant: Season pheasant with salt and pepper. Place pheasant, thyme, bay leaf, and butter in a vacuum bag and seal on the highest setting. Cook en sous vide at 160 degrees for 25 minutes. Transfer bag to large bowl of ice water to cool for 15 minutes. Remove breast from bag and discard remaining contents. Cut breast into 3/4-inch cubes. Cover with damp paper towel and refrigerate until ready to use.

2. Make the Shallots: Preheat oven to 350 degrees. Toss shallots with oil and salt. Place in a small roasting pan or ovenproof skillet; roast until very soft, about 1 hour. Remove from oven and let cool completely. Remove papery skin and thin translucent skin from shallots. Cut into 1/2-inch cubes. Refrigerate until ready to use.

3. Make the Cider Gel: Line a 4 1/2-by-6-inch shallow pan with plastic wrap. Peel and core apples and cut into 2-inch pieces. In a small saucepan, bring apples, cider, salt, and agar-agar to a simmer over medium heat; simmer until apples are soft, about 15 minutes. Transfer to a blender; blend until smooth. Strain through a fine mesh strainer into prepared pan. Transfer to refrigerator, taking care to keep level; let chill until set, about 2 hours. Cut into 1/2-inch cubes; refrigerate until ready to use.

4. Prepare the Oak Branch Skewers: Using a vegetable peeler, pare one end of each twig to about thickness of a bamboo skewer with leaves on opposite end.

5. Make the Dry Tempura Base: In a medium bowl, mix together flour, baking powder, and cornstarch; set aside.

6. To Serve: In a medium bowl, gently fold sparkling water into 75 grams (2.6 ounces) dry tempura base with a fork. Line a baking sheet with a double layer of paper towels; set aside. Heat oil in a medium saucepan until it reaches 375 degrees on a deep-fry thermometer.

7. Gently thread 1 shallot piece onto each oak branch, followed by 1 cube of cider and 1 cube of pheasant; season with salt and pepper. Dredge in flour, shaking off any excess.

8. Dip shallot, cider, and pheasant on skewer into tempura batter so that it just covers the cubes; let any excess drip off. Holding leaf end of skewer, immediately immerse battered cubes in oil until crisp and lightly browned, about 3 minutes. Drain on paper-towel-lined sheets and season with salt and pepper.

9. Ignite leaves with a kitchen torch and quickly extinguish; serve while leaves are still smoldering.