Special equipment: cheesecloth
Make paneer: Line a colander with a triple-layer of dampened cheesecloth, leaving a 2- to 3-inch overhang. Place the colander in the sink. Heat the milk in a large non-reactive saucepan over medium heat, stirring frequently to make sure the milk doesn't scorch on the bottom, until the milk comes to a simmer. Turn off the heat and gently stir in 3 tablespoons lemon juice. The milk should start separating into solid curds and a yellowish watery whey. If it doesn't, add a little more lemon juice. Let sit for about 5 minutes in the pot to continue separating, then gently pour into the cheesecloth-lined colander. (If the curds are still very small after 5 minutes then reheat the milk mixture over medium heat and simmer to increase the curd separation).
Rinse briefly with cold water to remove any lemon flavor. Gather up the sides of the cheesecloth, twist into a ball, and squeeze to wring out as much liquid as possible. Open up the cheesecloth, and mix 1/4 teaspoon salt evenly into the cheese curds. Squeeze into a ball again and wring out any remaining moisture. Flatten the cheesecloth ball into a 3/4-inch thick disc and place on a plate. Weigh down with another plate topped with a heavy item such as a large can. Refrigerate for at least 1 hour and up to overnight, then carefully cut the paneer into 3/4-inch cubes.
Meanwhile, bring a large pot of generously salted water to a boil. Have a large bowl of ice water nearby. In batches, blanch the spinach for about 1 minute in the boiling water and quickly transfer with a spider or slotted spoon to the ice water. Drain the cooked spinach. Place all of it in a blender and puree until mostly but not completely smooth. Reserve.
Rinse the blender carafe and puree the tomatoes; reserve. Rinse the carafe again and puree the garlic and ginger with 1/4 cup water; reserve.
Line a plate with paper towels. Heat 2 tablespoons ghee in a large nonstick skillet over medium to medium-high heat. Add the paneer cubes and brown well on 2 to 3 sides, about 5 minutes total. Remove to the lined plate and reserve.
Add another 2 tablespoons ghee to the skillet over medium-high heat. Add the cumin seeds and stir until the seeds start to darken and smell toasted, 10 to 30 seconds. Add the serrano chile, onion, and 1/2 teaspoon salt. Cook until the onion is dark brown and soft, about 10 minutes. Turn down the heat if the onion starts to burn.
Add the ginger-garlic paste, turmeric, cayenne, and half the garam masala. Stir for about 2 minutes, then add the tomato puree, stirring continuously, until the mixture starts to look dry, about 6 minutes. Add the spinach puree, sugar, 1/4 cup water, 1 1/2 teaspoons salt and the remaining garam masala. (The mixture will be quite thick.) Simmer for 8 minutes, then stir in the heavy cream and remaining 2 tablespoons ghee. Fold in the browned paneer cubes and simmer to warm the paneer through and to thicken the heavy cream, an additional 4 minutes.
Serve with steamed basmati rice or Indian flatbread and lemon wedges on the side.
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