In a small bowl combine the goat cheese and cream. Stir until smooth and creamy. Add lemon juice, zest and black pepper, stir to combine and set aside.
Preheat oven to 300 degrees. Line a baking sheet with paper towels and set aside.
Heat oil over medium heat in a 9-10" skillet. Add the butternut squash and kosher salt and sauté for 5 minutes until squash is slightly softened. Stir in the green onion and shallot and sauté for an additional 2-3 minutes. Remove from heat and stir in the lemon zest. Set aside.
Mix the flour, cayenne pepper and black pepper together and sprinkle over the butternut squash. Stir until well combined. Add the eggs and stir to combine - until the batter is just moist.
In a heavy bottomed skillet (cast iron or enamel coated like Le Creuset works great) heat the olive and canola oil until very hot, but not smoking. Spoon heaping tablespoons of butternut squash batter into the pan and flatten with the back of a spoon. Don't crowd the pan -- work with only 3-4 fritters at a time. Cook for 3-4 minutes until browned and crispy then carefully flip the fritters and brown on the other side. Transfer the fritters to the paper towel lined pan and keep warm in the oven, while you continue to make the rest of the fritters.
Serve fritters hot. Have your guests top the warm fritters with a spoonful of the lemon chèvre which gets delightfully gooey.