How to Make It
Prepare the Tots: Preheat oven to 400°F. Line a large rimmed baking sheet with parchment paper, and spray with cooking spray. Fill a medium bowl with ice water. Set aside.
Bring a medium saucepan of water to a boil over high. Add broccoli, and cook until bright green, about 2 minutes. Transfer to bowl of ice water, and let chill 5 minutes. Drain well, and pat very dry.
Place broccoli in a food processor, and pulse until finely chopped, about 7 pulses. Transfer to a large bowl, and stir in eggs, panko, Parmesan, scallions, parsley, basil, salt, and pepper until fully combined. Scoop about 1 tablespoon of broccoli mixture into your hands, and gently press into a nugget shape. Place on prepared baking sheet, and repeat with remaining broccoli mixture.
Lightly coat tots with cooking spray, and bake in preheated oven until browned and crispy, 20 to 25 minutes, turning halfway through.
Meanwhile, prepare the Dipping Sauce: Place cream in a 2-cup microwavable measuring cup, and microwave on HIGH until hot, about 1 minute, stirring after 30 seconds. Gradually stir in extra-sharp Cheddar, continuing to stir until melted and smooth. Serve immediately with Tots.