Combine the buttermilk (reserving 1/4 cup for the dressing), sage leaves, garlic and peppercorns in a deep dutch oven set over medium-low heat. Add the chicken and poach the chicken, turning it every couple of minutes, until completely cooked through. Be careful as you poach the chicken. You DO NOT want the buttermilk to curdle and if it comes to a simmer, you will run the risk of curdling. It is OK if you find that the buttermilk is separating a tad. This is normal. Adjust the heat as necessary if you find the mixture is reaching a simmer. It will take between 25-30 minutes for the chicken to cook fully.
While the chicken is poaching, prepared your dressing.
In a small bowl, stir together the remaining 1/4 cup buttermilk, Greek yogurt, sour cream, capers, chopped gherkins, and lemon zest. Season to taste with salt and black pepper. If you are looking for a thinner dressing, add a tad more buttermilk, whole milk, or lemon juice.
At this point, you may toss the mixed greens, radishes, and radicchio with the dressing or serve it on the side. Serve both with sliced buttermilk-poached chicken and enjoy!