In a bowl, combine one tablespoon of the olive oil with the red potatoes.
Season with one teaspoon of lemon pepper seasoning and a sprinkling of salt and pepper.
Stir to make sure all the potatoes are evenly coated.
Line a grill pan or your grill grates with aluminum foil and spray with nonstick cooking spray (or use nonstick foil.) This part is optional (see notes below.) Pour potatoes into grill pan.
Preheat gas or charcoal grill to a medium-high heat (about 350F.) Place pan on grill.
Cover grill and allow potatoes to cook for 12-15 minutes, making sure to occasionally stir the potatoes for even cooking.
Meanwhile, combine green beans with one tablespoon of olive oil, slices of butter, one teaspoon of lemon pepper seasoning, diced shallots and minced garlic with a sprinkling of salt & pepper. Stir well.
After the potatoes have cooked for at least 12 minutes, add green beans to grill basket and stir gently
Cook for about 8-10 minutes longer (until potatoes and green beans are tender.)
The reason why you want to line your grill pan or you grill grates with aluminum foil is because we are adding adding butter while it is cooking and if butter drips into the grill, it can cause flare ups and you don't want to burn your potatoes. If you are lining your grill grates, do this before turning on and preheating your grill.
If you don't want to line anything with aluminum foil, you don't have to. You can add the 4 tablespoons of butter to the hot vegetables after you take them off the grill and stir to combine. Just make sure to spray your grill basket with nonstick cooking spray.
You DO NOT need a grill pan for this. You can use a disposable aluminum pan or even heavy duty aluminum foil. Just make sure you also spray it with nonstick cooking spray just to make sure there is no sticking.
To make in the oven, preheat the oven to 400F degrees. Add the potatoes to a bowl and toss with ½ the olive oil and lemon pepper seasoning. Roast in pan (lined with nonstick aluminum foil) for 15 minutes. Add the green beans, garlic, shallots to same bowl and toss with remaining olive oil and lemon pepper. Add to the baking sheet with the potatoes. Roast together for 10 minutes. Melt the butter and coat the roasted vegetables with the butter mixture and serve.