Rinse turkey, pat dry, and place, skin down, on a board; sprinkle meat side with chopped parsley and thyme, season with salt and pepper.
Cover with cheese and prosciutto, overlapping slices.
Starting with a long edge, roll up turkey firmly, jelly roll style; overlap 3-4 sprigs down length of roll; tie roll securely with string at 2" intervals. (At this point, you may cover and refridgerate until next day.)
Place turkey, thyme side up, in slow cooker; pour in broth and wine, then cover and cook until meat in thickest part is very tender when pierced (9-10 hours).
Carefully lift turkey to a warm platter and keep warm.
Skim and discard fat from cooking liquid; blend in cornstarch (blended with water).
Increase cooker to HIGH; cover and cook, stirring 2 or 3 times, until sauce is thickened.
Remove and discard strings and thyme sprigs from turkey; slice meat 1/4" thick.