Fill a pot 3/4 of the way with cold water. Add 1 tbs of salt to the pot along with the peeled and chopped sweet potatoes and golden potatoes. Place the pot on high heat and boil for 15-20 minutes until potatoes are tender (a knife or fork should go clean through a potato piece if you poke one, if there's still resistance, it's not cooked all the way. P.S. It's really important to put the potatoes in cold water because it keeps them from getting sticky and gummy.
When the potatoes are done, reserve 1 cup of the boiling water and strain off the rest of the water. Mash the potatoes with a masher or large fork. Add 2 tbs olive oil, 1/2 tsp salt and gradually add the reserved boiling water 1/4 cup at a time. How much water you use depends on how thick you like your mashed potatoes; I like mine thick and use about 1/2 cup. Set the potatoes aside.
Heat a deep skillet to medium high heat. Add 1 tbs of olive oil to the warm skillet. Add onions to the pan and let them cook for about 2 minutes (occasionally stirring) until lightly golden brown. Add the chopped carrots to the onions, stir and let them cook for 3 minutes. Add the chopped mushrooms to the pan, stir and let cook for another 2 minutes. Add 2 tsp of thyme to the veggies, along with 1/2 tsp salt and 1/4 tsp black pepper. Pour the cooked veggies into your baking dish (I use a 3 cup glass Pyrex dish).
Place the skillet back on the burner and turn the heat up to high. Add 1 tbs of olive oil to the pan. Add the ground turkey, smoked paprika, cayenne, 1/2 tsp salt and 1/4 tsp black pepper to the skillet. Use a rubber spatula or wooden spoon to break the meat into smaller bits as it cooks, about 3-4 minutes. You'll know it's cooked when you don't see any more bright pink meat. Add the thyme to the cooked meat and stir until evenly combined. Turn off the heat and pour the cooked meat into the cooked veggies.
Stir the meat and veggies together in the baking dish until everything is evenly combined. Top the meat with the sweet potato mash and use a spoon or rubber spatula to spread the potatoes into an even layer.
Set the oven to your high broil setting. Broil the shepherd's pie for 5-10 minutes (depends on how hot your oven is) until the top of the potatoes are golden brown with some small charred spots. Enjoy!