Step 1 : Introduction to the question "Whose Valyrian Steel Sword was melted down to create Oathkeeper and Widow’s Wail? "
Jaime provides Brienne of Tarth with Joffrey's sword, which she names "Oathkeeper", new armour and Podrick Payne to serve as her new squire. As she leaves, she almost breaks down in tears, and looks back at Jaime while on her horse, which causes Jaime to realise her feelings for him.