First, make a roux for the gumbo base: In a large saucepan over medium heat on the stove, warm the vegetable oil. Stir in the flour and cook for 15 to 20 minutes, getting your spoon into the corners of the pan and stirring about every 15 seconds (do not leave the stovetop). The roux should simmer gently for the first 10 minutes. After 10 minutes, reduce the heat to low. Stir almost constantly for 5 to 10 minutes more, watching carefully so the roux doesn’t scorch.
When the roux turns the color of a walnut shell, stir in the onion, celery, and bell peppers. Continue to cook for 10 minutes more, stirring frequently. Add 1 teaspoon salt, ½ teaspoon pepper, the cayenne, thyme, and bay leaves and stir to thoroughly combine all of the ingredients. Add the chicken stock and bring to a boil, stirring constantly. Reduce the heat to medium and simmer until slightly thickened, 10 to 12 minutes. Remove from the heat.
Prepare the grill for indirect cooking over medium-high heat (450° to 500°F) and preheat the grill pan over direct heat.
In a medium bowl whisk the olive oil with a pinch of salt and pepper. Add the shrimp and toss to coat. Place the pot of gumbo base over indirect medium-high heat to keep warm while you grill the shrimp and sausage.
Spread the sausage slices in a single layer on the grill pan and grill over direct heat, with the lid closed, until golden and heated through, 1 to 2 minutes, turning once. Add the sausages to the gumbo base.