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Preheat oven to 425 degrees.
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Add the cut squash and chopped onion along with the salt, pepper, paprika, coconut oil, and 1 tablespoon of butter to a baking dish. Bake for 20 minutes until tender and ever so slightly golden on the edges. Let the veggies cool while you cook the pasta and make the sauce.
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Boil the water and cook the noodles until al dente, not cooked all the way through. Drain and set off to the side.
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Once the squash has cooled, add it along with the pumpkin puree and 1 cup of milk to a food processor. Puree until completely smooth.
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In a large pot, melt the 2 tablespoons of butter over medium heat. Once melted, whisk in the butter. Reduce heat to low, pour in the 2 cups of milk. Whisk to combine. Increase heat to medium, keep whisking. Once the sauce thickens, add the cheeses (reserving about 3/4 cup of cheese for the topping), mustard, and the puree. Whisk to combine.
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Preheat oven to 325 degrees F. Grease the inside of a 9 inch springform pan.
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After the cheese completely melts and the sauce is combined, remove from heat. Add a spoonful of the sauce to the beaten eggs, whisk to combine. Pour the egg mixture into the sauce and whisk vigorously to combine.
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Pour the noodles into the springform and cover with the sauce. Give it a little mix/toss to combine and spread the noodles out. Sprinkle the cheese on top of the noodles and sauce. Cover with breadcrumbs.
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Bake for 45-50 minutes until set and golden.
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Let cool for at least 20 minutes before slicing and serving.