Place cocktail potatoes in a baking pan and mix with olive oil and coarse salt. Bake in preheated oven to 350°F (180°C) until soft.
If you prefer, you can cook them in salted boiling water instead of baking them.
Melt butter and oil over hot water. Stir in cream cheese and milk. Add creamy aji sauce to taste, grated Parmesan cheese and chopped thyme and parsley. Correct seasoning.
Place cooked potatoes on a serving dish and serve with cheese sauce.