Add the artichoke to the skillet, then add a few large handfuls of spinach. Cook, stirring and tossing frequently, until the spinach has wilted. Repeat with remaining spinach. Continue cooking for about 12 minutes, stirring frequently, until the spinach has dramatically reduce in volume and very little moisture remains in the bottom of the pan.
Warm 2 tablespoons olive oil a large skillet over medium heat. Once the oil is shimmering, add the chopped onion and ¼ teaspoon salt. Cook, stirring often, until the onion is tender and translucent, about 4 to 5 minutes. Add the garlic and cook, stirring constantly, until fragrant, about 30 seconds.
Rinse out the food processor and return it to the machine. Pour half of the cottage cheese (1 cup) into the processor and blend it until smooth, about 1 minute. Transfer the mixture to large mixing bowl. No need to rinse out the bowl of the food processor this time; just put it back onto the machine because you'll need it later.
Preheat oven to 425 degrees Fahrenheit. To prepare the tomato sauce, first pour the tomatoes into a mesh sieve or fine colander and let them drain off excess juice for a minute. Transfer drained tomatoes to the bowl of a food processor. Add the basil, olive oil, garlic, salt and pepper flakes. Pulse the mixture about 10 times, until the tomatoes have broken down to an easily spreadable consistency. Pour the mixture into a bowl for later (you should have about 2 cups sauce).