Whisk the warm water, saffron threads, yeast, and 1 teaspoon of the sugar in a medium bowl. Let stand until foamy, about 10 minutes.
Combine the flour, oil, grapefruit juice and zest, salt, eggs, yeast mixture, and the remaining sugar in the bowl of a stand mixer fitted with the dough hook. Mix on low speed, scraping the bowl occasionally, until the dough comes together in a firm, stretchy mass, about 7 minutes.
Turn out onto a clean work surface and knead to form a tight ball, about 2 minutes. Lightly oil the mixer bowl, return the dough to it, and cover with a clean kitchen towel. Let rise in a warm spot until doubled in size, about 1 hour.
Line a half sheet pan with parchment paper. Turn the dough out onto a clean work surface and divide it into six equal pieces. Roll each into a 12-inch-long strand.
Braid three ropes, tucking in the ends. Repeat with the other 3 strands of dough to form a second loaf. Transfer both braids to the prepared pan, spacing them at least 5 inches apart.
Cover with a clean kitchen towel and let rise in a warm place until puffed and the volume increases by about a third, roughly 45 minutes.
Position a rack in the center of the oven and preheat the oven to 400°F. Beat the remaining egg with a couple teaspoons of water or milk and gently brush it over the loaves to lightly coat. Sprinkle with the sesame seeds.
Bake until browned and well risen, approximately 20 minutes. Cool completely on a wire rack before slicing.