Prepare the dough by combining 2 cups flour with 4 tablespoons melted butter and 1/2 teaspoon salt in a large bowl. Gradually add water (about 1/2 cup) and knead until smooth and elastic, about 8 minutes. Cover with damp cloth and rest for 30 minutes.

Boil 4 medium potatoes until tender, about 15 minutes. Drain, cool slightly, and mash coarsely. Heat 2 tablespoons vegetable oil in a pan over medium heat. Add 1 teaspoon cumin seeds and let them sizzle for 10 seconds.

Add 1 minced onion to the pan and sauté until golden, about 5 minutes. Add 1 tablespoon minced ginger, 2 minced garlic cloves, and 1 minced green chili. Cook for 1 minute until fragrant.

Add 1 teaspoon coriander, 1 teaspoon garam masala, 1/2 teaspoon turmeric, and 1/2 teaspoon cayenne pepper. Stir for 30 seconds. Add the mashed potatoes, 1 cup green peas, salt to taste, and 2 tablespoons chopped cilantro. Mix well and cook for 3 minutes. Remove from heat and let cool completely.

Divide dough into 6 equal balls. Roll each ball into an oval about 6 inches long. Cut each oval in half to create two semi-circles.

Take one semi-circle and form a cone by bringing the straight edges together, overlapping slightly. Seal with water. Fill the cone with 2 tablespoons of potato mixture, leaving space at the top.

Moisten the open edge with water and press firmly to seal, creating a triangular shape. Repeat with remaining dough and filling.

Heat oil in a deep pan to 350°F. Carefully slide 3-4 samosas into the hot oil. Fry on medium-low heat for 10-12 minutes, turning occasionally, until golden brown and crispy. Drain on paper towels. Serve hot with tamarind chutney and mint sauce.