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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.
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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.
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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.
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Remove the potatoes from the oven and let cool slightly. Keep the oven on.
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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.
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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.
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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.