Preheat the oven to 350°F.
Alternatively, heat a gas grill so it holds 350°F temperature when the lid is closed. (On a 3-burner Weber, turn the middle burner off, and the top and bottom burners to low.) Experiment with your grill, getting to know where the hot spots are—grills are all different, to say the least.
Lightly spray a seasoned 10-inch cast iron skillet with cooking spray.
In a medium bowl, melt the butter with oil, over a pan with gently simmering water, or on top of the heated grill. Let cool a minute or so. Using a spoon, stir in the sugar and honey.
Sift or whisk the flour with the baking soda and salt, until you are sure the soda and salt are evenly distributed. Add the egg and vanilla to the sugar mixture, then immediately stir in the flour mixture, stirring until the batter is smooth. Stir in the chocolate morsels and walnuts. Spread the batter in the prepared skillet.
If using a regular oven, bake 18 to 20 minutes.
If using a grill, bake 25 to 30 minutes, with the lid closed, keeping the grill temperature as close to 350°F as possible. About every 5 minutes, rotate the skillet 90 degrees. Baking time will depend on how often you open the grill lid.
Bake until the middle of the cookie is set, no longer raw. It will continue to cook in the pan, so, when the cookie is done in the middle, remove from oven or pull it off the grill.
Let cool 10 minutes before cutting into wedges.