In a skillet over medium high heat, sauté the chicken breasts in the olive oil until browned, about 7 to 9 minutes; remove from skillet, drain of excess oil, and set aside, keeping warm.
In a large heavy saucepan, heat the milk and chicken broth over medium temperature.
Add the tarragon (crushing it a bit in your hand, first), garlic, scallion, white pepper, and curry powder, and bring to a light simmer.
Add 3/4th of the Swiss cheese gradually (reserving the remaining 1/4 for garnish), stirring constantly, until well-incorporated.
Gradually add the white wine, then the sour cream.
Using an immersion blender, whir the soup until all ingredients are smoothly incorporated (soup may have a tendency to separate before this point); alternately, you can pour it all into the blender or food processor.
Put the soup back in the saucepan if you removed it, then add the ham, and the cooked chicken breast; season to taste with salt and freshly ground pepper.
Simmer on low heat for 10 minutes.
Garnish with reserved grated Swiss cheese and basil and serve immediately.