Heat the milk in a large pot over medium heat, stirring often, until the milk foams up and nearly boils. Remove the pot from the heat immediately.
Add the lemon juice or vinegar. Stir gently just until distributed. Let the pot rest for 10 minutes while the curds form.
Place a colander inside a large bowl. Drape a tightly woven cloth inside the colander. Carefully pour in the curds and whey. If the bottom of the colander is submerged in whey, transfer the whey to another bowl or heat-resistant jars. Let the curds sit in the colander and continue to strain over the bowl for 30 minutes.
Gather up the edges of the cloth to form a ball of paneer and turn and squeeze out as much whey as you can. Reserve the whey for another use.
Place the cloth-wrapped ball of paneer between two cutting boards or plates. Place a heavy weight on top and allow the paneer to rest for 1 to 2 hours. Chill in the refrigerator to firm up the cheese and eat within a few days.