Bring the khoya to room temperature. If it is soft and moist, crumble it thoroughly by hand; if it is firm, grate it using a box grater. Measure 1/2 cup grated khoya and knead it well with the heel of your palm for 2 to 3 minutes until smooth and lump-free.
Add maida, a small pinch of salt and cooking soda to the kneaded khoya. Mix gently to form a crumbly mixture. If the khoya is dry, sprinkle water or milk very little by little to form a smooth, soft, non-sticky dough. If the khoya is already moist, do not add any liquid. Cover and let the dough rest for 5 to 10 minutes.
In the meantime, prepare the sugar syrup. In a pan, combine sugar and water. Bring to a boil over medium heat for about 5 minutes until it reaches a sticky consistency (it should feel sticky and glossy between your fingers; no string consistency is required).
Add cardamom powder and saffron strands if using. Turn off the flame and let the syrup cool down to warm. (Add 1 to 2 tsp lemon juice if you want to avoid sugar crystallization).
Mandatory testing step for beginners: Pinch a tiny ball of dough, roll it smooth and crack-free. Heat oil or ghee in a kadai on low to medium heat. Check the oil temperature by dropping a tiny speck of dough; if it rises slowly to the surface, the temperature is ideal. Drop the test ball into the oil.
Observe the test ball: It should double in size slowly and stay crack-free without dissolving. If the ball dissolves, the soda is slightly high—knead in a teaspoon of maida with a sprinkle of water. If cracks appear on the fried ball, moisten the dough with a teaspoon of milk or water and knead briefly.
Divide the rest of the dough into small, smooth portions and roll gently between your palms into crack-free mini balls. Grease your palms with a drop of ghee if needed. Keep them covered with a moist cloth so they do not dry out.
Reheat the oil on medium-low flame. Gently drop the balls into the oil without crowding. Do not touch them for the first 30 seconds. Gently swirl the oil with a slotted ladle so the jamuns rotate and brown evenly on all sides. Fry patiently on medium-low heat until evenly golden brown all over.
Remove the fried jamuns with a slotted spoon, drain excess oil on a kitchen paper towel and immediately transfer them into the warm sugar syrup. Let them soak for 1 to 2 hours until they plump up and absorb the syrup. Serve warm or at room temperature!