Combine garlic, chile pepper, cumin, paprika, black pepper, cayenne, and salt in a mortar; grind with a pestle until it forms a paste. Add olive oil and mix dersa well. Heat a large saucepan over medium heat and stir-fry dersa until fragrant, 2 to 4 minutes. Add potato halves and stir to combine with the dersa. Stir in tomato paste. Pour in enough water to just cover the potatoes and bring to a boil. Reduce heat and simmer until potatoes are tender, about 40 minutes. Ladle potatoes into a serving bowl. Spoon any remaining sauce over the potatoes.