This side quest can be done during chapters 2, 3, 4, 6, 7, 8, 11, or 13.
Also, to make life easier for yourself, make sure you have 1 piece of cheese on you as you will need it during the side quest. These can be bought at the Milk Barn from Keith.
You have to wait until at least 6pm on a rainy evening when Emily is at home. It has to be raining because Emily goes out to eat on non-rainy evenings. Go to Emily's house which is located not too far from the Milk Barn and go inside. Speak to Emily and after the conversation York will be tasked with finding out what the missing ingredient is. Now speak to Emily again and hand over the cheese. After another scene the side quest is finished and you're rewarded with the trophy.