Heat the oven to 375°F. Lightly grease a 12-cup muffin tin with a little olive oil.
Warm the olive oil in a skillet over medium heat. Add the butternut squash and cook for 6 to 8 minutes, stirring occasionally, until the cubes are just tender. Set them aside to cool slightly.
While the squash cooks, make the relish. Combine the cranberries, maple syrup, and water in a small saucepan. Bring to a gentle simmer over medium heat, then cook for 8 to 10 minutes, stirring now and then, until the cranberries burst and the mixture thickens. Stir in the orange zest and set aside to cool.
In a large bowl, combine the ground turkey, breadcrumbs, egg, onion, thyme, salt, and black pepper. Add the cooked squash and mix gently until everything is evenly distributed. Avoid overmixing so the muffins stay tender.
Divide the turkey mixture among 8 cups of the prepared muffin tin, filling each cup evenly. Bake for 20 to 25 minutes, until the centers reach 165°F.
Let the muffins rest in the tin for 5 minutes, then lift them out carefully. Spoon the cranberry relish over each muffin before serving.