In the bowl of a stand mixer fitted with a paddle, mix together yeast, milk, saffron, and 1 tsp. sugar; let sit until foamy, about 10 minutes. Stir in the remaining sugar, along with the flour, salt, and 2 eggs. Mix on low speed until dough forms and gathers around the paddle. Replace paddle with dough hook and add butter; knead on medium-high speed until dough pulls away from sides of bowl, 8 minutes. Transfer dough to a large bowl greased with oil and cover with plastic wrap; let rest in a warm place until doubled in size, 1 hour.
Divide dough into 32 pieces and roll each piece into an 8"-long rope. Form each rope into an S shape and then roll each end into a tight spiral. (See Shaping Saffron Buns for illustrated step-by-step instructions.) Place shaped dough pieces 2" apart on parchment paper–lined baking sheets; cover with plastic wrap and let rise in a warm place for 30 minutes.
Heat oven to 400°. Uncover the dough pieces and place a raisin at the center of each of the spirals. Lightly beat remaining egg with 1 tbsp. water and brush each bun with egg mixture. Bake until buns are golden brown and cooked through, 16 minutes. Transfer buns to a wire rack and let cool for at least 10 minutes before serving.