The ornamental design for brown bag beverage cooler, as shown and described.
FIG. 1 is a perspective view of a brown bag beverage cooler, as shown with a beverage container placed therein;
FIG. 2 is a right-hand side view thereof;
FIG. 3 is a left-hand side view thereof;
FIG. 4 is a rear view thereof;
FIG. 5 is a front view thereof;
FIG. 6 is an enlarged top view thereof; and,
FIG. 7 is an enlarged bottom view thereof.
The broken line showing of a beverage container is included for the purpose of illustrating environmental structure and forms no part of the claimed design.