Make the whipped goat cheese: Beat together the goat cheese, cream cheese, lemon juice, olive oil, and salt with a fork or hand mixer until fluffy and smooth. Spread onto serving plates and refrigerate until ready to serve.
Heat olive oil in a medium skillet over medium heat. Add shallot and cook until softened, about 3 minutes. Add garlic and cook 1 minute more.
Stir in harissa paste, cumin, and smoked paprika. Cook for 1 minute until fragrant.
Pour in crushed tomatoes and season with salt. Simmer for 8-10 minutes until sauce thickens slightly.
Create 4 wells in the sauce using a spoon. Crack one egg into each well. Cover the pan and cook for 5-7 minutes until whites are set but yolks are still runny.
Remove plates with whipped goat cheese from refrigerator. Drizzle with olive oil and sprinkle with za'atar.
Carefully spoon the harissa sauce and eggs over the whipped goat cheese. Garnish with fresh mint or parsley. Serve immediately with toasted sourdough bread.