Preheat oven to 350°. Cut butternut squash in half down the center, from top to bottom. Scrape out pulp and seeds. Place on a sheet pan and drizzle interior with olive oil. Sprinkle with ½ tsp salt, ¼ tsp pepper, and rub to coat the inside of squash. Place cut-side down on the sheet pan and bake of an hour, or until flesh is very tender.
Meanwhile, make pasta dough: place flours and salt in a food processor. Pulse several times to combine.
Add egg yolks, olive oil, and sourdough discard to food processor. Blend for 30-60 seconds until a rough dough forms. If dough does not start to come together, add water by the teaspoon until it does.
Transfer dough to a work surface and knead for about 10 minutes, until dough is fairly smooth. Cover in plastic wrap and leave to rest (at least 30 minutes).
Meanwhile, make pasta filling: heat 1 tbsp olive oil in a skillet over medium heat. Add garlic and cook briefly until fragrant. Add kale and cook, stirring occasionally, for 3-4 minutes until wilted and starting to lightly brown. Move to a bowl.
Add ½ tsp salt, ¼ tsp pepper, ricotta, and Parmesan to bowl with kale. Mix together.
When butternut squash is done roasting, scrape the flesh into a bowl. Add 2 cups to a blender, along with yogurt, stock, cumin, paprika, ½ tsp salt, ¼ tsp pepper. Blend until smooth. Set aside.
Heat a large pot of salted water over high heat.
Divide pasta dough into 4 equally sized pieces. Flatten each into a round puck. Cover with plastic or a towel.
Roll out one portion of pasta at a time, keeping the others covered. Set a pasta roller to its widest setting and pass the dough through. On a lightly floured surface fold the sheet into thirds from the short ends to make a rectangle of dough about the width of the pasta roller. Flatten dough with your hand or a rolling pin and pass through the roller again on the widest setting. Repeat folding and feeding through the widest setting one more time, or until the dough is smooth and even.
Roll out dough twice through each of the following settings until dough is about 1 mm (Refer to pasta roller manual for guidance. For a KitchenAid pasta roller, roll out to setting 5 or 6).
Cut dough into squares (they should be around 4x4 inches, give or take). Top each with 2-teaspoon mounds of kale-cheese filling. Brush the top of the dough with water, around the mounds of filling. Fold one corner of the dough over to the opposite corner to make a triangle. Press down to seal around filling. Trim edges if desired.
Gently flatten the filling with your fingers. Fold up the bottom third of the triangle, from the base towards the tip. Wrap the dough around a finger to make a ring, with filling on the inside, and press the ends together to seal. Place shaped tortellini on a floured surface.
Transfer soup from blender to a saucepan and place over medium-low heat. Stir occasionally.
When pot of water is boiling cook tortellini for 3-4 minutes, gently stirring occasionally, until al dente. Drain and return to pot.
Divide soup until bowls and top with tortellini. Sprinkle with pepitas and thyme. Drizzle olive oil over the top.