Preheat oven to 350°F
Using a very sharp knife, cut a pocket down the long side of the chicken breast, taking care not to cut through the ends.
Stuff 1/4 of the blue cheese in each chicken pocket, pressing cut side to seal cheese into pocket.
Make sure outside of chicken breast is very dry. Use paper towels to dry if needed.
Season chicken with salt and pepper
Place two slices of prosciutto on a cutting board, overlapping long sides slightly. Place chicken breast, top (presentation) side down in the middle of the prosciutto slices perpendicular to the prosciutto. Using slight pressure, bring the bottom ends of the prosciutto up over the chicken breast and press to adhere.
Roll chicken breast up over the top ends of the prosciutto so the ends of the prosciutto overlap and seal the chicken nicely. Keep firm pressure as you are rolling the chicken up so the prosciutto sticks well.
Heat a skillet over medium-high heat and add 1 Tbsp of the olive oil. When hot, add the chicken breast presentation side-down to the pan and cook until prosciutto is nicely browned, about 3-5 minutes. Flip chicken carefully and cook the other side until lightly browned, 3-5 minutes. Remove chicken to a sheet tray and place in preheated oven to finish cooking. Cook chicken for approximately 15-20 minutes, until prosciutto is crispy and a thermometer, inserted into the thickest part of the chicken shows 160°F and juices run clear. Remove from oven, cover chicken with foil and let rest. Chicken will continue to cook slightly during this time.
Add remaining olive oil to the hot pan. Reduce heat to medium-low and add shallots. Cook for 2-3 minutes, stirring often. If desired, reserve a few shallot slices for garnish. Add wine and chicken broth and bring to a slight boil, scraping any browned bits in the pan.
Whisk together the flour and milk; whisk into the broth/shallot mixture. Return sauce to a boil and reduce heat and simmer, stirring occasionally, until sauce is thickened.
Slice chicken at an angle, if desired, or serve whole, spooning shallot sauce over chicken. Top with reserved shallot slices and additional cracked pepper.