Preheat gas or charcoal barbecue grill to medium-high heat. (You can hold your hand there about 3 seconds at that heat.)
Peel sweet potatoes and cut into slices about 3/4 inch thick.
Lay slices on a cookie sheet, then measure 1/4 cup vinaigrette and brush each side of sweet potatoes with dressing, seasoning each side with salt and freshly ground black pepper after you brush on the dressing.
Grill the sweet potato slices, cooking about 4-5 minutes on first side, then rotating to cook 3-4 minutes on that side.
When you have nice grill marks on the first side (or when sweet potatoes are getting dark on that side) flip the sweet potatoes over and cook about 7-8 minutes more on the second side, or until sweet potatoes feel tender when pierced with a fork.
Total grilling time will be about 15-20 minutes, but I started taking them off the grill as they felt done, and the larger pieces took more time.
Let grilled sweet potato slices cool for 10-15 minutes, then cut into cubes and place in salad bowl.
Add sliced green onions, chiffonade basil strips, and chopped thyme and gently combine with sweet potatoes.
Stir in the other 1/4 cup of vinaigrette, using as much as you need to moisten the salad (you may not need all the dressing, depending on how wet you like your salads.)
Gently stir in the crumbled feta, season salad with salt and freshly ground black pepper to taste, and serve salad at room temperature.
