Special equipment: a pastry bag fitted with a medium tip
For the poppy seed crackers: Preheat the oven to 300 degrees F.
Pulse the flour, poppy seeds, onion powder and kosher salt together in a food processor to combine. Add the butter and pulse until the mixture resembles coarse meal. Add 1/4 cup of the half-and-half and process until the dough begins to clump together.
Lay out a large piece of parchment paper and dust it with flour. Turn the dough out onto the parchment, form it into a flat rectangle and then roll it out to approximately 10 by 17 inches. Freeze until firm, about 10 minutes.
Trim the dough to straighten the edges, then cut into 2-by-1-inch rectangles. Brush the tops with the remaining tablespoon of half-and-half and sprinkle with the flaky sea salt. Transfer the crackers on the parchment to a baking sheet and bake until crisp and light golden brown, about 30 minutes. Cool on a rack. (The crackers can be made up to 1 day ahead and stored in an airtight container at room temperature.)
For the egg mousse: Pulse the eggs, mayonnaise, lemon juice and some kosher salt in a food processor until very smooth. Add the chives and pulse to combine. Transfer to a pastry bag fitted with a medium tip and refrigerate until ready to use.
To assemble: Pipe the mousse onto the crackers. Top with a small dollop of caviar and some chives. Serve immediately.