For the croquettes: Melt the butter and olive oil in a medium saucepan over medium heat. Saute the shallots and garlic for 1 minute. Add 1/4 cup of the flour and cook until it forms a paste, 2 to 3 minutes. Slowly whisk in the milk and bring to a boil. Add the ham and lower the heat, keep stirring until the mixture is thick and releases from the sides of the pan. Season with salt and pepper add the thyme.
Transfer the mixture to a bowl. Cover with wax paper and let chill for at least 5 hours.
Preheat oil to 350 degrees F in a deep pot.
Roll the croquettes into 1-ounce balls. Bread using the 3-step bread method: use the remaining 1/2 cup flour, and then the eggs, and then the breadcrumbs. Roll the croquettes in the flour, shaking off excess, then roll in the egg, then roll in the breadcrumbs making sure to coat completely. Fry until golden brown, and then transfer to a paper-towel-lined plate. Transfer to a plate and serve with the saffron aioli on the side.