Melt butter in a saucepan over high heat; add sweet potato, salt, and 1/4 cup water. Cook and stir just until sweet potato is soft, about 5 minutes.
Heat olive oil in a skillet over low heat; add onion, carrot, garlic, and ginger; cook and stir until onions are brown, about 10 minutes.
Place chicken stock, split peas, and marjoram in a pressure cooker. Cover pressure cooker with lid and cook soup according to manufacturer's instructions, about 10 minutes. Remove from heat; open pressure cooker carefully.
Stir cooked sweet potatoes and onion-carrot mixture into split pea mixture. Garnish with Parmesan cheese; season with paprika and lemon pepper.
