Preheat your Z-Grills (preferably with branded oak pellets) or other wood pellet grill to 225 degrees Fahrenheit.
Rub the haddock fillets with oil, then season both sides of each fillet with salt and black pepper.
Place the grill mat on the grates and transfer the fish to the grill mat.
Close the grill’s lid and cook for 50-55 minutes or until the internal temperature reaches 145 degrees Fahrenheit.
At the 25-minute mark, fill a large skillet with water and bring it to a boil on your stovetop. Salt the water once boiling.
Add the green beans and cook for 3 minutes. The beans are ready when they are tender and bright green.
Drain the green beans and set them aside.
Melt the butter in the same skillet used to cook the green beans. Do this over medium heat.
Add the shallot and sauté for 2-3 minutes or until softened, fragrant, and slightly brown at the edges.
Add the green beans, peas, salt, and black pepper. Cook for 2-3 minutes or until the peas are warmed through. Set aside but keep warm.
Heat the oil for the sauce in a saucepan over medium heat.
Add the shallot and sauté for 2 minutes or until softened.
Pour in the wine and lemon juice.
Next, add the sugar and salt. Bring to a simmer over medium-high heat and simmer for 3 minutes or until reduced by half.
Stir in the cream, return the sauce to a simmer, and simmer for 2 minutes.
Remove the sauce from the heat and slowly stir in the cubes of cold butter. Add one cube at a time, stir until melted, and repeat until you incorporate all the butter.
Add black pepper to taste.
Divide the green beans and peas between four plates.
Drizzle white wine sauce over the green beans and peas.
Place a smoked haddock fillet on top of each serving of green beans and peas, finish with more sauce (if desired), and serve.