Pit nectarines, reserving pits; coarsely chop one nectarine. In a 2- to 3-quart pan over high heat, combine pits and chopped nectarine with honey, thyme sprigs, and 2 cups water. Boil, stirring occasionally, until liquid is reduced to 1/3 cup, about 20 minutes; pour through a fine strainer into a glass measure. Let syrup cool about 10 minutes.
Whisk lemon juice and mustard into syrup; slowly pour in oil, whisking until emulsified. Add salt and pepper to taste.
Slice remaining nectarines and combine in a large bowl with endive, chives, and shallot. Gently mix in dressing.
Divide salad among six plates. Drape prosciutto equally over servings and sprinkle with thyme leaves, arugula, and almonds.