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 with aluminum foil and spray with nonstick cooking spray (or use nonstick foil).
The reason why you want to do this is later we will be adding butter and if butter drips into the grill, it can cause flare ups and you don't want to burn your potatoes.
Place pan on grill.
Grill should be on a medium heat setting (about 350F-400F degrees.)
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.
Add green beans to grill basket and stir gently.
Cook for about 8-10 minutes longer (until potatoes and green beans are tender.)
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.