Directions

1. Heat 1/2 cup water in a small saucepan or a tea kettle over high until a thermometer registers 205°F, about 3 minutes. Remove from heat; stir in 2 tablespoons tea leaves. Cover and let steep 3 minutes. Pour tea through a fine wire-mesh strainer into a small heatproof bowl; discard tea leaves. Add raisins, and let soak, uncovered, at room temperature, until plump, at least 30 minutes or up to 1 hour.
2. Meanwhile, fill a small bowl with ice and water; set aside. Bring brown sugar, star anise, cinnamon, and remaining 6 cups water to a boil in a high-sided medium skillet over high. Stir in 2 tablespoons kosher salt and remaining 1/2 cup tea leaves. Reduce heat to medium-low, and add chicken and eggs. Cover and cook, undisturbed, 10 minutes. Transfer eggs to a work surface. Lightly crack shells all over using the back of a spoon; return eggs to poaching liquid. Flip chicken; cover and cook, undisturbed, until a thermometer inserted in thickest portion of chicken registers 155°F, about 10 minutes. (Temperature will continue to rise to 165°F as chicken rests.) Transfer chicken to a plate, brush off any large tea leaves, and let rest 10 minutes. Transfer eggs to bowl of ice and water; let cool 5 minutes. Discard poaching liquid.
3. Meanwhile, transfer raisins and soaking liquid to a blender. Add vinegar, thyme, honey, Dijon, pepper, and remaining 1/4 teaspoon kosher salt; process until smooth, about 30 seconds. With blender running, drizzle in oil, and process until thick and glossy, about 30 seconds; set aside. Add up to 1 tablespoon water, 1 teaspoon at a time, to thin if desired.
4. Peel eggs, and cut in half lengthwise. Toss together lettuce, walnuts, shallot, and 1/2 cup vinaigrette in a large bowl. Slice chicken breasts 1/4 inch thick. Serve chicken and eggs over salad; garnish with smoked sea salt and additional thyme leaves and pepper. Serve with remaining vinaigrette on the side.