Clean, trim and half the cutlets. If they still remain thick, lightly pound them out between two sheets of parchment paper.
Warm the EVOO in a large skillet over high heat. Season the chicken cutlets with salt and pepper. Cook the chicken until golden and cooked fully through, about 2 to 3 minutes per side. Transfer the chicken to serving plate. Tent with foil to keep warm.
Turn the stove heat to medium, add the shallot and the garlic and cook until tender, about 2 minutes.
Deglaze the pan with the white wine. Scrape all the brown bits from the bottom of the pan and mix in. Cook until the wine is almost evaporated.
Add the chicken broth and saffron threads, bring to a simmer and reduce for 10 minutes. You’ll want the broth to reduce during this time. Add the cream, salt, and pepper. Stir to combine and simmer for 1 minute to blend the flavors. Pour the sauce over the chicken.