Bring a large pot of water with 1 Tablespoon salt to a boil over high heat.
Cook potatoes by piercing the potatoes with a fork and microwaving for 5-6 minutes until tender. You should be able to easily cut through the potatoes with a knife.
Peel the skin from the potatoes and then pass the potatoes through a ricer into a larger bowl.
Meanwhile, combine the flour, kosher salt, and spices in a medium sized bowl.
Add the flour mixture, eggs, and pumpkin puree to the potatoes. Using your hands, gently combine the ingredients until the dough is smooth and soft. Try to add as little flour as needed to keep the dough from sticking. Allow to rest for 10 minutes.
Lightly dust your work space with flour. Divide dough into 4-6 pieces. Roll each ball into a long snake about 1/4 inch thick. Cut your rope into 1 inch pieces. Place the finished gnocchi onto parchment paper or cookie sheets lightly dusted with flour.
Cook the gnocchi in batches in the salted boiling water. Cook for 2-3 minutes until gnocchi rises to the surface. Using a large slotted spoon remove gnocchi. Repeat as needed until the gnocchi is all cooked.
For the parmesan sauce:
For the sauce, melt the butter over medium heat. Add flour and stir until completely mixed.
Add milk a little at a time and stir well after each addition. Cook and stir over medium heat until thick and bubbly.
Add shredded cheese and stir until completely melted and incorporated. Add fresh herbs and stir, cooking for 1 minute more.