Rub the butter into the dry mixture by hand until it resembles breadcrumbs.
Whisk together the eggs and milk in a separate bowl and add to the dry mixture.
Combine the mixture with a whisk until a smooth, lump free batter forms. Set aside.
To make the chai syrup, heat the sugar, chai tea and rosewater in a small pot and bring to a boil. Let the sugar melt completely and let it slightly reduce for a few minutes. Keep the syrup warm.
Heat enough oil in a pot so that the gulab jamun can deep fry properly.
As soon as the oil is hot enough, carefully start dropping spoonful's of the batter into the oil and let it fry for a few minutes each side until golden brown. Remove, place onto kitchen towel and let the excess oil drain off.
Once all the gulab jamun is fried, pour the warm syrup over to let it soak up the syrup before serving.