Add halved red and Yukon Gold potatoes to a large pot; fill with cold water 3" higher than potatoes. Bring to a boil, then add quartered sweet potatoes. Return to a boil and cook approx. 8 min, until potatoes are slightly softened in center, but still firm enough for grilling and handling. Drain well, being careful not to break potatoes.
To prepare for grilling, combine 1/2 c olive oil, mustard and spices and rub over potatoes on all sides. On a hot grill, mark potatoes on all sides; working in small batches and not overcrowding to avoid burning or breaking them. Toss green beans in 2 T olive oil to coat and add a pinch of salt and pepper. Grill just until blistered. Gently toss beans and potatoes with Warm Dijon Bacon Dressing, almonds, herbs and green onions, garnishing with Parmesan. Serve warm.
Warm Dijon Mustard and Bacon Dressing
In a skillet over medium heat, cook bacon until almost crisp. Remove from heat and let bacon cool slightly in pan, including fat. Add oil, vinegar and mustard to pan with bacon, whisking to combine. Add lemon juice, salt and pepper, then whisk until emulsified. Keep warm until ready to add to potatoes.
* To make this recipe vegetarian and vegan, omit bacon.