Preheat the oven to 400 degrees.
Prepare the artichokes by first cutting ¾ of the stem off.
Clip the pointy tops of all the leaves with kitchen scissors.
Cut the artichoke in half, you will see the choke in the center. Using a spoon, scrape out the spikey textured center because it is inedible.
Repeat for the rest of the artichokes.
In a large roasting pan or baking dish, add the artichoke halves and diced potatoes.
Top with olive oil and 2 teaspoons of salt and 1 teaspoon of pepper.
Place in the oven for 10 minutes uncovered. Then cover with foil and cook for 20-25 more minutes.
While those are roasting, prepare the sauce in a food processor.
Place the chives and parmesan in the processor and pulse until finely chopped.
Add in the yogurt, water, lemon juice, 2 teaspoons salt, 1 teaspoon pepper and blend well.
Place in a bowl and refrigerate.
Remove the artichokes and potatoes, top with sliced red onion.
To serve, dip the leaves in the sauce and enjoy!