In a small bowl whisk to combine the soy sauce, a 1/4 cup of the olive oil, steak spice, and honey. Place the mushroom caps in a large resealable container and pour the mixture over top. Toss to coat and transfer to the fridge. Marinate for 8-12 hours.
When the mushroom caps are marinated, place the mayo in a bowl and add the smoked paprika. Stir to combine and cover and transfer to the fridge until ready to serve.
½ cup mayo, ½ tsp smoked paprika
Arrange the radicchio wedges on a small baking sheet and drizzle with the remaining olive oil. Sprinkle with salt and place on a hot BBQ grill or cast iron griddle. Briefly grill the radicchio wedges on both sides just long enough to char slightly. Return the radicchio to the baking sheet and set it aside.
¼ cup + 2 tbsp olive oil, 1 head radicchio, ½ tsp kosher salt
Place the mushroom caps on the grill or griddle, gill-side-down. Cook for 5 minutes then flip and cook for another 5 minutes. Return the portobello caps to gill-side-down and top with the smoked gouda. Cover the caps with either a large domed pot lid if cooking on a griddle, or place the lid on the BBQ if using a grill. Cook until the cheese has melted.
85g (3oz) smoked gouda
While the burgers are cooking, toast the burger buns. Slather both the top and bottom buns with the smoked paprika mayo and top the bottom buns with a handful of Hickory Sticks. Place the portobello burgers on top and place 2 wedges of the radicchio on top of the burgers. Place the top buns on top and serve immediately.
4 burger buns, 1 cup Hickory Sticks **
Notes
** If Hickory Sticks are unavailable in your country, use BBQ or bacon or another smokey potato chip in their stead.