Preheat oven to 450°. Scrub outside of potatoes under running water then dry with a towel. Cut potatoes into small chunks (maybe something like half of a golf ball) and place in bowl. Toss with a few tablespoons of canola oil (or another oil with high smoke point) and then scoop onto a large baking sheet. Turn each potato chunk skin side down.
Using pinches of each ingredient, scatter kosher salt, pepper, chili powder, and thyme over the oily tops of all the potatoes until each piece has an evenly dispersed dusting of tasty herbs. Place the potatoes in the preheated oven for 45 minutes or until you see the chunks turning golden brown. Remove and cool before adding other ingredients.
While the potatoes are cooking (or while you’re waiting for them to cool) combine the green onion, roasted reds, kalamatas, artichoke hearts, parsley, and crumbly cheese chunks to the large bowl you would like to serve the dish in.
Decide what is best for you to create an emulsified vinaigrette in: blender, food processor, Magic Bullet* (or other mini-food processor with speedy blades). If using a blender or food processor, add all the vinaigrette ingredients and then slowly drizzle in the oil while the machine is running. If using a Magic Bullet, just combine all the ingredients and blend until creamy.
Combine the potatoes with vegetables and pour in the dressing. If you want a quick hot dish, stir to thoroughly coat the ingredients and serve warm. If you're interested in a cool dish (or wish to serve later), chill for at least 4 hours or overnight before serving.