Heat oven to 375 degrees Fahrenheit. Lightly oil each butternut squash half with 1 tablespoon olive oil and season each half with 1/2 teaspoon kosher salt. Place butternut squash halves (flesh side down) on a rimmed baking sheet and roast in heated oven for 1 hour, or until flesh is soft and a fork can easily pierce the flesh.

(Prepare tortellini dough as below while butternut squash is roasting.)

Remove butternut squash from oven and allow to cool for about 15 minutes before scooping the flesh out and discarding the skins. Add butternut squash flesh to a food processor with 1 cup grated parmesan cheese, 1 egg, and remaining 1/2 teaspoon kosher salt. Pulse until well combined and smooth. Set aside until pasta dough is ready.

To a large stand mixer fitted with a dough hook, add all-purpose flour, semolina flour, and salt. Mix to combine. With mixer running on medium add 3 eggs, olive oil, and milk. Mix until the dough comes together into a rough ball. It may be necessary to add a little bit of water: put the 1-2 tablespoons of water into a small cup and add just a splash or two at a time. Wait 10-15 seconds and repeat if the dough still has not come together. (You will be able to tell when it is ready!) Turn out dough onto a smooth flour-covered surface and knead for 1-2 minutes. Cover with a kitchen towel and allow to rest at room temperature for at least 30 minutes.

Fill a small bowl with water.

When dough has rested, spread a bit of flour on a large cutting board or dough board (I use this marble dough board). Cut the dough ball into four or five large pieces and leave one pasta ball on your board, storing the rest under a kitchen towel to prevent drying. Use a pasta roller to roll out remaining pasta ball into a sheet (I like to roll mine to the #5 thickness on my KitchenAid pasta roller attachment). Use a 3" round pastry cutter (biscuit cutter) to cut out as many circles from your dough as you can fit. Set aside the remaining dough under the kitchen towel as you can reuse this as long as it does not dry out too much.

Add about 1/2 teaspoon of filling to the center of each dough circle. Dip your finger in the bowl of water and run along the outer edge of the dough circle. Fold half the pasta over the filing and seal, creating a half-moon shape. Fold the top round edges of the half-moon shape back on itself and twist the underside around your finger. (See post above for step-by-step photo instructions!) Set aside on a baking sheet covered in a bit of flour and repeat with remaining dough.

Add garlic cloves to food processor and pulse until finely minced, scraping down the sides of the bowl and necessary. Add baby arugula and walnuts and pulse until well chopped. With food processor running, stream in olive oil through the top hole until mixture is homogenous. Add parmesan cheese and greek yogurt and pulse just until combined. Season with salt and pepper and set aside.

Bring a large pot of salted water to a boil. Cook tortellini for about 2-3 minutes. Toss in a large bowl with a small splash of pasta water and some arugula pesto and serve with more fresh parmesan.