Preheat the broiler. Toss the broccoli with salt, pepper and 2 tablespoons of olive oil and place on a sheet pan lined wth parchment. Broil six inches from heat source for about 7 – 9 minutes, turning, until lightly browned and charred. Remove, set aside, and cool.
Lower the oven to 375F / 190C. Rinse and dry the potatoes. Rub with a little olive oil and place on a baking sheet. Roast for about 30 minutes, or until softened but not totally baked through. They need to be firm enough to hold up when cut.
As the potatoes bake, prepare the filling: Heat 2 tablespoons olive oil in a large skillet over medium flame and cook the onions until soft, about 7 – 8 minutes, stirring. Add the garlic and stir around for a minute to soften. Transfer the mixture to a mixing bowl.
Remove the potatoes from the oven and let cool slightly. Keep the oven on.
Cut the potatoes in half lengthwise to get two long, oval halves. Score the flesh with a paring knife and using a teaspoon scoop out as much of the flesh as possible without tearing the potato skins. Set the flesh aside in a separate bowl.
In a medium mixing bowl, whisk together the Greek yogurt, mustard, egg, remaining olive oil, crumbled feta and lemon zest. Add about half of the potato pulp and the broccoli-onion-garlic mixture and stir gently to combine. Season with salt and pepper to taste.
Place the potato halves on an oiled baking dish and spoon the filling into each skin so that it is a heaping mound. Place back in the oven and bake for about 20 minutes, or until lightly golden and bubbly. Remove and serve hot.