Make the cheese: Line a colander with 8 layers of cheesecloth, draping it over the sides, and set in a sink. In a large, nonstick pot over medium-high heat, bring the milk to a full boil, stirring often with a wooden spoon to prevent it from scorching on the bottom. Stir in the lemon juice, then lower the heat to medium-low and cook without stirring just until large curds form, about 30 seconds. Remove from the heat and set aside, without disturbing for 2 minutes, then pour the milk mixture into the colander. Gather the corners of cheesecloth together and gently squeeze out some of the excess liquid. Tie the opposite corners of the cheesecloth together to make a sack, and hang it from a large kitchen spoon suspended over a deep bowl. Set aside at room temperature until the excess liquid has thoroughly drained from the cheese, about 1½ hours. Transfer the sack to a plate, untie the cheesecloth, and loosely drape the corners over the cheese. Place a large heavy pot on top of the cheese, then set aside at room temperature to compress for 30 minutes more. Remove the pot and unwrap the cheese. Cut into ½-inch-by-1-inch pieces.
In a 12-inch nonstick skillet, heat the ghee over medium. Working in batches, add the cheese and fry until golden brown, about 6 minutes. Using a slotted spoon, transfer the cheese to a plate and set aside; reserve the skillet with ghee.
Make the spinach: In a blender, combine the garlic, ginger, chile, and ¼ cup water; purée into a smooth paste. Return the skillet with ghee to the stove, and heat over medium-high. Add the ginger-garlic paste and cook, stirring, until fragrant, about 30 seconds. Add the spinach, salt to taste, and cook, stirring often, until the spinach wilts, about 1 minute. Reduce the heat to medium-low, cover, and cook, stirring often, until the spinach is very soft, about 15 minutes. Stir in the cream, garam masala, and cayenne. Add the cheese to the skillet, cover, and continue cooking until the liquid thickens and spinach is soft, about 15 minutes more. Serve with flatbread or rice.