Using a whisk, combine honey, soy sauce, 1/4 cup salt and water. The brine needs to taste like sweet sea water. (Multiply as necessary to fully submerge turkey in a container). Add turkey breast, cover and refrigerate for 24 hours. Rinse turkey under running water before cooking and pat dry.
Preheat oven to 250°F.
Lightly season turkey breast with salt and generously season with ground pepper. In a medium-sized Dutch oven or oven-proof pot, add the turkey breast. Then add the rosemary, thyme, ginger, potatoes, carrots, garlic heads, fennel and jalapeños. Fill pot with oil until all items are submerged. Cover and slow bake for 2 hours, turning the breast and vegetables occasionally. Internal temp of turkey should reach 150°F.
Remove pot from oven. Let pot cool for 1/2 hour with turkey and vegetables remaining inside. Using tongs, remove turkey from oil and let drain. Transfer to plate and rest for an additional 10 minutes.
Using a slotted spoon, remove carrots, fennel, potatoes and jalapeño peppers. Transfer to medium mixing bowl and toss with lemon juice and zest. Season with salt and pepper. Set aside.
Heat a large sauté pan over medium-high heat. Place turkey breast skin side down in pan and sear for approximately 1 minute. Flip and repeat on second side.
To serve, transfer turkey breast to a large, warmed serving platter. Surround the turkey with vegetables.
TIP: The cooking oil can be reused in other recipes. Strain all solids and boil to get out all the water. Refrigerate in an airtight container.
