For the Salted Caramel Syrup:
Combine the sugar, water, and the corn syrup in a large saucepan and stir with a wooden spoon over medium heat until sugar is dissolved & turns clear. Cover the saucepan and let it cook over medium heat for 3 minutes. Remove the lid & increase the heat to medium-high. Bring to a boil. Don't stir from this point on, but swirl the liquid around the pan so the caramel doesn’t burn. Continue to cook until the caramel turns an even amber color (5-10 minutes?) then remove from the heat and let stand for about 30 seconds. Pour the heavy cream SLOWLY into the mixture. The mixture will bubble up significantly and is extremely hot. Stir the mixture, again being careful. Add the butter, lemon juice, and salt. Stir until combined. Measure 1/2 cup into a Pyrex measuring cup. Stirring occasionally, allow to cool until thick like molasses and warm to the touch, about 20 minutes. Store any extra in an airtight container in the fridge.
For the Salted Caramel Frosting:
Cream butter and cream cheese on medium, until smooth. Add one cup of powdered sugar and beat until combined. Add salted caramel. Add more powdered sugar for a stiffer frosting (I liked mine loose for this recipe). Set aside.
For the Apple Cups:
Combine apples, spices, butter, sugar and pecans with a fork or your fingers. Set aside. Spray a 12-muffin muffin tin with nonstick spray or line with cupcake liners. Flatten each roll out and add a heaping tablespoon of mixture in the middle. Set it inside the muffin tin. I covered my rolls with plastic wrap (covered in cooking spray) for about an hour. Alternatively, you could just pop them in the oven as-is for a crispier crust. I wanted mine to be fluffy. Bake at 350º F for 12-15 minutes or until edges are golden brown. Remove from the oven & allow to cool a few minutes before removing from the pan. Frost & enjoy! Makes 12 apple cups. Stored un-eaten (if any) muffins in an airtight container on the counter for up to 2 days.