Heat your oven to 425˚F. Give the squash a good scrub then cut in half lengthwise. Trim the ends then cut each half into ¼” thick slices. Place on a baking sheet and toss with the olive oil, smoked paprika, and salt. Roast until starting to brown, about 25 minutes.
While the squash is roasting, heat a small skillet over medium. Add the hazelnuts and toast until starting to brown. Remove from heat and stir in the maple syrup and salt. Toss to coat and transfer to a plate to cool. Wipe out the skillet, return to heat, and fry the eggs.
Next, cook the pasta according to the package directions and make the sauce. To make the sauce, combine the goat cheese, milk, salt, garlic, and zest in a bowl. Stir/whip together until well combined.
When the squash is done, remove from the oven and add the hazelnuts/basil to the sheet tray and toss the squash with the nuts/basil.
Drain the pasta, saving a bit of pasta water, and return the pasta to the pot. Add in the goat cheese mixture and stir to combine. Add in a splash of pasta water if needed to coat the noodles. Divide into bowls and top each bowl with an egg and the delicata squash.