PREHEAT OVEN TO 375 DEGREES. WHISK TOGETHER FLOURS, SALT, AND BAKING SODA IN A SMALL BOWL; SET ASIDE. PUT BUTTER AND SUGARS INTO THE BOWL OF AN ELECTRIC MIXER FITTED WITH THE PADDLE ATTACHMENT; MIX ON MEDIUM SPEED UNTIL PALE AND FLUFFY. REDUCE SPEED TO LOW. ADD EGG AND VANILLA; MIX UNTIL COMBINED. MIX IN BANANA. ADD FLOUR MIXTURE; MIX UNTIL JUST COMBINED. STIR IN OATS, CHOCOLATE CHUNKS, AND WALNUTS.
USING A 1 1/2-INCH ICE CREAM SCOOP, DROP DOUGH ONTO GREASED* BAKING SHEETS LINED WITH PARCHMENT PAPER, SPACING ABOUT 2 INCHES APART. BAKE COOKIES, ROTATING SHEETS HALFWAY THROUGH, UNTIL GOLDEN BROWN AND JUST SET, 12 TO 13 MINUTES. LET COOL ON SHEETS ON WIRE RACKS 5 MINUTES. TRANSFER COOKIES TO WIRE RACKS; LET COOL COMPLETELY. COOKIES CAN BE STORED IN AIRTIGHT CONTAINERS UP TO 2 DAYS.
* FOR THOSE NEW TO BAKING..IT MEANS BRUSH YOUR BAKING PANS LIGHLY WITH SOFTENED OR MELTED BUTTER OR SPRAY WITH BAKING SPRAY LIKE CRISCOS OR PAM.