Season chicken with about ¾ teaspoon salt and pepper on either side.
Heat oil in a skillet over medium heat.
Add chicken and sear on both sides until the internal temperature reaches 165 F.
Remove the chicken from the skillet and slice. Set aside.
In a clean skillet, add butter and melt over medium heat. Add the garlic.
Sprinkle with flour and stir until a paste forms, about 1 minute.
Add the heavy cream and cream cheese and stir constantly to combine. Allow the mixture to thicken into a sauce, which should take about 3 to 5 minutes.
Once the sauce has thickened, season with the remaining ¼ teaspoon each of salt and pepper. Remove the sauce from the heat and stir in ½ cup of shredded Parmesan.
Scoop about ¼-inch of bread out of each half of French bread loaf.
Transfer the semi-hollowed bread halves to a foil-lined baking sheet. Spread the sauce thinly over the bread halves, then layer on the sliced chicken.
Add another layer of sauce, then top with remaining ½ cup Parmesan.
Bake the bread until the cheese on top is melted, about 10-12 minutes.
Let cool slightly, then slice and serve the garlic bread.