Place the flour and salt in the bowl of a food processor fitted with a metal blade. Pulse 2 to 3 ties to combine.
In a medium bowl, whisk the eggs and olive oil until well blended. Pour egg mixture into the bowl of the food processor. Pulse 10 times or so to blend the egg mixture and flour together. Steadily process the mixture for a few seconds at the end if needed. If the mixture is too dry, sprinkle water in while pulsing a few more times.
Turn the mixture out onto a well-floured surface. Knead to bring together and smooth the dough out. Place the dough in a bowl with a cloth bowl cover and let rest for at least 30 minutes or tightly wrap the dough in plastic wrap and place in the fridge for up to 1 to 2 days.
Roasted Carrot Puree
Adjust oven racks so that one is on the top third level and the other is on the bottom third level. Preheat the oven to 400 degrees F.
Cut the carrots in half lengthwise and divide between two sheet pans. Drizzle the oil over the carrots and sprinkle with salt, and pepper. Toss well and arrange the carrots on each pan into one layer.
Place the carrots in the oven and roast for 25 to 30 minutes, until tender and starting to brown.
Remove the carrots from the oven and set aside to cool. Once cool, transfer the carrots into the bowl of a food processor fitted with a metal blade. Add the goat cheese and blend until smooth.
Purée can be stored in an airtight container in the fridge until ready to use as a filling. It can be stored in the fridge for up to 4 days or frozen for future use. Place in fridge overnight to thaw filling if you freeze it.
For Ravioli
Make an egg wash by beating the egg in a small bowl with 1 tablespoon of water. Set aside.
Working with 1/4 at a time, roll the pasta to desired thickness, then cut the pasta sheets into 4 ½-inch strips about 12-inches long.
Place 1 teaspoon of filling on the pasta sheet, leaving about 1 ½-inches between each. Using a pastry brush or basting brush, brush the egg wash around the filling. Fold the top half of the pasta over the bottom, pressing out any air pockets. Using a pizza cutter or ravioli cutting wheel, cut out the ravioli and place on a well floured sheet pan. Toss the ravioli to lightly coat in flour to avoid sticking. Repeat with the remaining pasta and filling.
Bring a large pot of generously salted water to a boil. Working in batches, cook the ravioli for 2 minutes, then, using a slotted spoon or spider, transfer to a colander set over a bowl. While hot, toss the drained ravioli with sauce that it will be served in. Be sure the sauce is warmed.
Combine carrot tops, basil leaves, arugula, garlic, lemon juice, and almonds in a food processor fitted with a steel blade. Pulse until finely chopped.
Add red pepper flakes, season with kosher salt and black pepper. Pulse to incorporate.
While food processor is running, slowly add olive oil in a streaky stream.
Transfer to bowl and stir in parmesan and lemon zest.
Recipe Notes
Use pesto on pasta, sauteed vegetables, or in scrambled eggs!
Pesto can be stored in an air-tight container in the refrigerator for up to 1 week.
Try freezing pesto in ice cube trays for already portioned single servings to use all season. Frozen pesto will keep for up to 1 month.