Preheat the oven to 425°F. Spray a rimmed baking sheet with nonstick cooking spray, then spread the squash on the baking sheet. Drizzle with the 3 tablespoons olive oil, sprinkle with salt and pepper, and toss until the squash is evenly coated. Bake for 35 to 40 minutes, until the squash is nicely browned in spots and tender inside.
Meanwhile, make the Scallion Salsa Verde. Place the parsley, scallions, thyme, anchovies, capers, olive oil, lemon juice and zest, and red pepper flakes into the bowl of a food processor. Pulse several times, then let the motor run until it is pureed. Taste and add salt and pepper as desired (be generous with the pepper, but perhaps lighter on the salt thanks to the anchovies and capers). Transfer to a small serving bowl.
Then, make the Whipped Ricotta and Feta. Place the ricotta and feta into the (cleaned!) bowl of a food processor and pulse to combine. Add a nice amount of pepper. With the motor running, drizzle in the 1/4 cup olive oil until the mixture is fluffy and smooth. Taste and see if the mixture needs salt. Transfer to a small bowl.
Transfer the squash to a serving platter. Spoon the Whipped Ricotta and Feta in little mounds over the squash. Drizzle the squash with the Salsa Verde.