In a skillet over medium heat, begin browning the ground turkey, breaking it up into small pieces. As it's cooking, add the paprika, onion powder, garlic powder, dried rosemary, fennel, sea salt, and pepper. Stir the spices into the ground turkey while breaking it up into bite-size pieces. Continue to cook for 10-12 minutes or until the turkey is cooked through.
While the turkey cooks, begin cutting up the sweet potato, carrots, mushrooms, and broccoli. Once the turkey is cooked through, add the diced sweet potatoes and extra virgin olive oil. Stir to evenly coat the sweet potatoes with oil. Cover with a lid and continue to cook over medium heat for 5 minutes, stirring occasionally. Remove the lid and add the carrots, broccoli, and mushrooms. Replace the lid and cook for 3 minutes. Add the spinach and let cook for about 2 minutes or until the broccoli is bright green and the spinach has cooked down.
Remove the hash from the heat and serve.
Store leftovers in a covered container in the fridge for up to 4 days.