Peel shrimp, leaving tails intact. Starting at base of tail, insert a toothpick along the length of each shrimp to keep from curling, keeping part of the toothpick sticking out at tail.
Toss shrimp gently with 1 tbsp of the chili sauce. Set aside.
Cut chicken breasts into 1/2 inch thick strips, 2 to 3 inches long and toss in a separate bowl with remaining chili sauce.
Place one sheet of phyllo pastry on a board. Brush it lightly with melted butter. Cut in half lengthwise and then into thirds crosswise to make 6 squares.
Place one shrimp (on toothpick) about 1/2-inch up from bottom edge of one square, parallel to bottom and leaving tail shell hanging over left edge. Fold right side of square over shrimp meeting left edge. Roll up into cylinder. Brush outside of pastry with butter and place on parchment-lined baking sheet, seam-side-down.
Sprinkle with sesame seeds. Repeat with remaining shrimp, 3 sheets of phyllo and half each of the remaining butter and sesame seeds.
Repeat wrapping with chicken strips, leaving about 1/2-inch of chicken strip beyond left edge of phyllo square. Place on another parchment-lined baking sheet. Cover and refrigerate on baking sheets for up to 1 day. (These can be frozen for up to 2 weeks. Do not thaw before baking.).
For the dipping sauce, combine ketchup, soy sauce, vinegar, brown sugar and chili sauce in a small saucepan. Bring to a boil over medium heat, stirring often to dissolve sugar. Vigorously whisk in cubes of butter, a few at a time, until incorporated and smooth. Remove from heat and let cool. Stir in coriander, if desired. (Sauce can be refrigerated for up to 3 days.).
To serve, preheat oven to 450°F.
Bring dipping sauce to room temperature or warm slightly in a saucepan. Bake Shrimp Firecrackers for 5 to 7 minutes and Chicken Firecrackers for 10 to 12 minutes or until golden and shrimp are opaque and chicken is no longer pink inside. (Increase baking time by about 3 to 5 minutes if frozen.) Carefully remove toothpicks from shrimp. Place firecrackers on a warmed serving platter and serve with Spicy Dipping Sauce.