For the turkey: Pat the turkey legs dry with paper towels. Transfer the turkey to a baking sheet.
In a spice grinder, finely grind the thyme, sage and bay leaves. Rub the turkey with the herbs and sprinkle generously with the salt and pepper. Chill overnight, uncovered.
Preheat the oven to 325 degrees F. Heat the olive oil in a large pot over low heat to 170 degrees. Transfer the turkey to a 13-by-16-by-3-inch roasting pan. Pour the olive oil over the turkey. Cover the pan with foil and bake until the turkey is very tender, about 3 hours.
Let cool. Remove the skin and tendons. Reserve the meat and keep warm.
For the carrots and peas: In a large skillet, add the carrots and 1/4 cup water. Simmer over medium heat until the carrots are crisp-tender, about 2 minutes. Add the peas and increase the heat to high. Cook until the peas are crisp-tender and the liquid is reduced to about 1 teaspoon, about 1 1/2 minutes. Add the orange juice, butter and sugar, swirling the skillet to coat the carrots and peas. Cook until the liquid is reduced to a syrupy glaze, about 30 seconds. Season with salt and pepper.
Preheat the oven to 400 degrees F. Line a shallow baking pan with foil.
Prick each potato twice with a fork and bake in the prepared pan in the lower third of the oven until very tender, about 1 hour. Remove and cool slightly.
Warm the heavy cream. Halve the potatoes lengthwise and scoop out the warm flesh into a large bowl. Mash the potatoes and stir in the cream, butter and syrup. Season with salt and pepper.