In the bowl of a stand mixer, combine 1 tablespoon sugar, water, and yeast and let rest until foamy.
Meanwhile, heat butter, milk, and saffron in a saucepan over medium heat until butter is melted. Let cool until temperature is around 90°F, then strain and add yeast mixture.
Add flour and 1/2 cup sugar, and mix together with a dough hook until dough comes together cohesively and does not stick to the sides of the bowl.
Turn dough out onto a lightly floured surface and knead until dough is smooth and supple, about 2 minutes. Place dough in a greased bowl, cover, and let rise 1 hour.
Preheat oven to 400°F.
Divide risen dough into 16 pieces. Roll each piece into a 6-inch snake and form into an S-shape. Place each coil onto a parchement-lined baking sheet and let rise 1 hour.
Brush buns with beaten egg and place a raisin in the center of each coil, 2 per bun.