Combine water, sugar and corn syrup in stainless steel or enameled skillet with lid. Bring to a boil over medium heat, uncovered, stirring occasionally. Continue boiling sugar mixture, until it reaches light amber color. Reduce heat to medium low. Continue simmering sugar, stirring occasionally, until it reaches dark amber, about 15 minutes total.
Meanwhile, peel plantains and cut into 2-inch pieces. If using, cut shallots in half through root end; peel shallots; remove earthy roots, leaving just enough to hold shallot layers together.
When caramel reaches dark amber, remove from heat. Add 1 ½ cups broth, butter and salt, being careful of hot steam and caramel. Return skillet to medium heat, stirring constantly, until caramel is fully melted and sauce is boiling.
Add plantains and shallots to caramel sauce; stir briefly to coat; and return liquid to boil. Reduce heat to medium-low, cover skillet, and simmer for 12 minutes. Remove lid from skillet. Gently turn plantain pieces over. Continue simmering for 10 minutes; plantains should be tender, and easily pierced with tip of knife.
Whisk together corn starch and remaining 2 tablespoons broth until smooth. Add corn starch mixture to caramel sauce; gently stir until fully incorporated. Continue simmering plantains until sauce is thickened, about 1 minute. Add red wine vinegar; and season to taste with salt and black pepper. Serve plantains and shallots with caramel sauce spooned over top.