Preheat the oven to 425°F. Line a baking sheet with parchment paper and set aside.
Make the crabcakes: In a medium skillet, melt 2 tbsp. of the butter over medium heat until foamy. Add the onion and cook, stirring occasionally, for 3 minutes, until translucent. Add the garlic and stir for about 15 seconds, then transfer the mixture to a medium mixing bowl. Add the crab, 1⁄2 cup of the cracker crumbs, the eggs, Old Bay, salt, and pepper, and stir until well blended.
Put the remaining 3⁄4 cup cracker crumbs in a small bowl. Using a tablespoon, form the crab mixture into 36 balls, each about a packed tablespoon’s worth. Working with one ball at a time, flatten each into a roughly 1 1⁄2-inch-wide and 3⁄4-inch-thick disc, then dip it in the cracker crumbs on all sides and transfer to the prepared baking sheet. Repeat with the remaining balls and crumbs. (The crabcakes can be made to this point and refrigerated, covered, for up to 24 hours, or you can freeze them directly on the baking sheet, then pack them into an airtight container and freeze for up to 1 month.)
Brush the crabcakes all over with the remaining 4 tbsp. melted butter, then bake for 15 minutes (or slightly longer from frozen), or until well toasted.
Meanwhile, make the tartar sauce: In a small mixing bowl, stir together the mayonnaise, jalapeño, onion, cornichons, capers, lemon zest and juice, and salt and pepper to taste until well blended. Cover and refrigerate until ready to serve, or for up to 3 days.
Serve the crabcakes warm or at room temperature, with the tartar sauce dolloped on top or served alongside for dipping. (Cooled crabcakes can be refrigerated for up to 3 days and reheated for 5 minutes in a 425°F oven before serving.)