Place flank steak in a saucepan. Cover with water to 1 inch above steak; bring to a boil. Reduce heat to low; cover and simmer 1 hour or until steak is very tender and pulls apart easily. Transfer steak to a plate, reserving 1 cup cooking liquid. Cool steak completely; slice crosswise into thirds. Shred each piece; set aside.
Heat oil and annatto, if desired, in a small saucepan over medium heat 1 minute or until oil begins to bubble. Remove from heat; steep 10 minutes. Strain into a medium Dutch oven over medium-high heat; discard seeds. Add onion and bell pepper; cook 2 minutes or until softened. Add tomato, cumin, salt, black pepper, and garlic; cook 2 minutes or until mixture begins to thicken. Add steak, reserved cooking liquid, olives, and carrot, stirring to combine. Bring mixture to a boil; cover, reduce heat to low, and simmer for 10 minutes or until carrot is tender. Uncover, increase heat to medium, and cook 15 minutes or until almost all of liquid evaporates. Remove from heat; cool completely. Cover and chill 2 hours or, preferably, overnight.
Preheat oven to 400°. Line 2 large baking sheets with parchment paper.
Combine 1 teaspoon water and egg in a small bowl. Divide cold filling into 15 equal portions (about 3 generous tablespoons each). Keep filling chilled while making empanadas. Moisten edges of 1 dough disk with egg mixture; place 1 portion of filling in center. Fold dough over filling to form a half-moon shape. Gently press edges between thumb and index finger to form a border; crimp border using fork tines to seal. Place empanada on prepared pan. Repeat procedure with remaining dough and filling.
Lightly brush tops of empanadas with egg mixture. Bake at 400° for 23 minutes or until tops are golden brown, rotating pans in oven halfway through baking. Serve with hot sauce, if desired.