Preparation

Poach the shrimp

• In a 4-quart saucepan, combine the wine and Old Bay with 1-1/2 tsp. salt and 1 cup water; bring to a boil. Reduce the heat to low, add the shrimp, and poach until just cooked through, 2 to 3 minutes. Transfer the shrimp to a baking sheet and let cool in a single layer to room temperature. Cover with plastic wrap and refrigerate until ready to serve. Discard the poaching liquid.

Make the sauce

• Slice the peels away from the oranges. Working over a bowl, cut the segments free from the membranes, then squeeze the membranes to yield 1/4 cup juice. Coarsely chop 10 of the segments and set aside. In a food processor, combine the remaining orange segments and the orange juice with the tomatoes, tomato paste, sugar, coriander, chipotle, and 1 tsp. salt; purée until smooth.
• In a 4-quart saucepan, heat the butter over medium-high heat until the foam subsides. Add the onion and cook, stirring occasionally, until golden brown, about 3 minutes. Add the tomato mixture and bring to a boil over medium heat. Reduce the heat to low and simmer for 5 minutes to meld the flavors. Cool to room temperature. Add the horseradish and refrigerate until cold, at least 2 hours.

Serve

• Peel the shrimp, leaving the tails intact. If using the balsamic glaze, generously drizzle it down the inside of four Champagne coupes or martini glasses. Season the sauce with more salt and horseradish to taste. Divide the sauce among the glasses. Garnish with the reserved chopped orange segments, place 4 to 5 shrimp around the rim of each glass, and serve.

Make Ahead Tips

The shrimp may be poached up to 1 day ahead and refrigerated, covered.

The sauce may be made up to 1 day ahead.