Add the potatoes to a baking sheet. Drizzle on olive oil, along with the oregano, paprika, salt and lemon juice. Using your hands or a spatula, toss the potatoes until evenly covered in the lemon juice, oil and spices.
Place in the oven for 20 minutes. After 20 minutes, remove from the oven and toss. Add the broccoli florets, minced garlic, parsley and sliced lemon. Once again, using a spatula, mix until the potatoes and broccoli are evenly dispersed and coated in the garlic and parsley. Add more oil or salt as desired at this point.
Place in the oven for an additional 20 minutes until the potatoes are crispy and the broccoli is cooked through. Enjoy with vegan whipped feta dip or as a side dish as desired.