Crumble cheese into a medium bowl. Roughly chop tarragon and rosemary; add to cheese. Mix well.
Split chicken breast lengthwise about 3/4 through the breast; do not cut in half.
Coat 9″ x 13″ baking pan with the olive oil.
Arrange chicken breasts in olive oil coated pan.
Fill with cheese/herb mixture and set aside.
In a medium saucepan, melt butter over medium high heat. Whisk in flour. Slowly pour in milk and whisk for about 4 to 5 minutes until slightly thickened. Slowly pour in lemon juice and lower heat to medium. Whisk constantly for another 3 to 4 minutes until mixture thickens.
Pour sauce over cheese stuffed breasts.
Bake at 375 degrees for 45 to 50 minutes until chicken registers 160 degrees with meat thermometer.