Prepare a grill by adjusting the grill grate so that it’s 4 to 5 inches from the flame or heat source. Heat a gas grill to high and a charcoal grill to medium hot (the coals should be covered with light ash, and you should be able to hold your hand just over the grate for no more than 3 seconds).Thread the tomatoes on parallel skewers.
Heat the oven to 375°F. Put the breadcrumbs on a baking sheet, drizzle with 2 Tbs. of the olive oil, and toss to distribute the oil evenly; season with salt and pepper. Bake in the middle of the oven, tossing occasionally, until the breadcrumbs turn golden brown, 8 to 10 minutes. Remove from the oven and let cool.
In a bowl, whisk the remaining 4 Tbs. olive oil with the balsamic vinegar. Season the vinaigrette to taste with salt and pepper.
Grill the skewered tomatoes, turning occasionally, until the skins darken and blacken in spots and begin to blister and shrivel, 5 to 7 minutes. Remove the tomatoes from the skewers and set aside.
Cook the orecchiette in boiling salted water until al dente. Drain and toss with the tomatoes and the vinaigrette, pour into a serving bowl, and garnish with the breadcrumbs and basil. Taste and season with more salt and pepper, if needed, and serve immediately.