You can use your favorite salad greens in place of the escarole. The dressing can be made four days ahead and stored in the refrigerator.
Let chicken stand at room temperature 30 minutes. Reserve 3 tablespoons buttermilk for dressing; place the rest in a large Dutch oven with sage and garlic.
Season chicken with salt and pepper and submerge in a single layer in buttermilk mixture. Cook over medium heat, stirring occasionally, until liquid is shimmering but not simmering, about 170 degrees on a thermometer. (Buttermilk will curdle slightly, so stir occasionally and adjust heat as necessary to maintain temperature.) Poach chicken, turning occasionally, until a thermometer inserted into thickest part of each breast registers 150 degrees, about 15 minutes (once liquid reaches temperature; chicken will continue to cook after poaching). Transfer to a dish and let cool; discard liquid. Slice chicken.
In a medium bowl, combine yogurt, shallot, cornichons, capers, lemon zest and juice, and reserved buttermilk. Season with salt. Arrange escarole on a platter; top with chicken slices, radishes, and almonds. Serve with dressing on the side.