Preheat your oven to 400°F and line a large sheet pan with parchment paper for easy cleanup.
Slice the halloumi into 1/2-inch thick rectangles and chop the red bell pepper, zucchini, and red onion into bite-sized pieces.
Place the vegetables and halloumi on the prepared sheet pan, then drizzle with olive oil and sprinkle with sea salt, black pepper, and dried oregano.
Toss the ingredients together until they are evenly coated in the oil and spices, then spread them out into a single layer.
Roast in the oven for 15 minutes until the vegetables are tender and the halloumi begins to turn a light golden brown.
Remove the pan from the oven and use a spoon to create two small wells among the vegetables, then carefully crack one egg into each well.
Return the pan to the oven for 5 to 7 minutes, or until the egg whites are fully set but the yolks remain slightly runny.
Drizzle the roasted mixture with fresh lemon juice and serve immediately with a side dollop of creamy Greek yogurt.