Place the potatoes in a large saucepan with enough water to cover. Bring to a boil, lower the heat and simmer until fork-tender, about 25 minutes. Drain and let cool slightly.
Meanwhile, in a small saucepan of boiling water, cook the broccoli until crisp-tender, about 5 minutes; drain. Finely chop the broccoli and place in a medium bowl.
Slice 6 potatoes in half. Scoop out half of the flesh from each piece and add to the broccoli. Peel and finely chop the remaining potato and add to the mixture. Add the cheese, 2 tablespoons yogurt and the jalapeno; mash coarsely and season with salt and pepper.
Preheat the oven to 425 degrees . Arrange the potato halves cut side down on a baking sheet and lightly coat them with cooking spray; invert and season with salt and pepper. Divide the stuffing among the potato halves. Lightly coat with cooking spray and sprinkle with chili powder. Bake until golden, about 20 minutes. Garnish with the remaining 1 tablespoon yogurt and more chili powder.