Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).

Wash and clean mushroom caps: Remove stems, scrape out gills, and rinse and pat mushrooms dry. Separate caps and stems and set aside.

Run water over two cedar grilling planks until soaked. Pat planks dry. Place in oven on middle rack and toast for five minutes.

Remove planks from oven and place side by side in a deep double roasting pan. Spray planks with cooking spray.

Finely dice mushroom stems along with one of the set-aside mushroom caps. 

Pour in white wine and hot sauce. Turn heat to medium-high for three minutes to allow wine to evaporate slightly. Add in panko crumbs, oregano, basil, salt, and pepper. Mix well. Turn off heat.

Place the six set-aside mushroom caps on the cedar planks. Drizzle with garlic-and-basil-flavored olive oil. Bake 10 minutes uncovered.

Remove pan from oven. Fill each mushroom cap with filling and return to oven for 10 minutes. Remove pan from oven and drizzle one tablespoon of teriyaki sauce over each stuffed mushroom. Return to oven and bake for a final 10 minutes.

Heat olive oil in a small frying pan and sauté diced onions and garlic for eight minutes. Add in chopped broccoli. Sauté, stirring, for three minutes.