For the poached chicken:

2 (8-ounce) boneless, skinless chicken breasts
1 medium yellow onion, quartered
2 bay leaves
10 whole black peppercorns
2 teaspoons kosher salt

For the shallot-tarragon jam:

2 tablespoons olive oil
1 tablespoon unsalted butter
1 1/2 pounds shallots, peeled, halved, and sliced 1/4-inch thick
1/2 teaspoon kosher salt
Freshly ground black pepper
1/4 cup plus 2 tablespoons white wine-tarragon vinegar
1/4 cup granulated sugar
2 tablespoons coarsely chopped fresh tarragon leaves

To assemble the sandwiches:

8 (1/2-inch thick) slices crusty bread, such as pain au levain