Authentic Indian Dal Makhani Recipe from a Restaurant

Name: Authentic Indian Dal Makhani Recipe from a Restaurant
Ingredients: 3/4 cup whole black lentils (urad dal sabut) (160-165 grams); 1 quarter cup of rajma (red kidney beans) Approximately 60-70 gram; 1 teaspoon kosher salt; 3.5 cups water (28 oz); 1 tablespoon ghee; 3 tablespoons butter divided, use salted butter if possible; 1 white onion (115 grams), finely grated; 2 teaspoons ginger garlic paste; 1/2 cup tomato puree; 1/2 teaspoon red chili powder; 1/4 teaspoon garam masala; 1/2 teaspoon salt to taste; 1.5 cups water (12 oz) as needed; 1/2 teaspoon sugar; 1/4 cup cream (60 ml); Butter for serving; Optional: a piece of charcoal to add a smoky taste to the dal