Prepare a medium bowl of ice water.
Place a medium saucepan of water over high heat. When the water boils, add 1 tablespoon salt and the broccoli florets and cook until crisp-tender, 1½ to 2 minutes. Immediately remove the broccoli with a slotted spoon to the ice water, reserving the broccoli water over low heat.
In a large skillet over medium-high heat, melt the butter. Add the red pepper, zucchini, ¾ teaspoon salt, and ¼ teaspoon pepper and sauté, stirring occasionally, until vegetables are softened and beginning to brown, 5 to 6 minutes. Reduce the heat to medium, add the scallions, onion powder, cream cheese, 1/2 cup of the Parmesan cheese, and 1/2 cup water. Cook, stirring often, until sauce is smooth and thick, 5 to 7 minutes.
Meanwhile, open the pack of shirataki noodles. Drain and rinse them, then place them in the hot broccoli water for 3 minutes. Drain, reserving ½ cup of the water. Set the noodles aside.
To the skillet of sauce, add the blanched broccoli and a bit of the reserved water if the sauce is too thick. Toss to coat, taste, then season with salt and pepper if desired.
To serve, add the noodles to the sauce, gently combine, then distribute among 4 plates, garnish with basil, and enjoy.