In a small bowl, mix the vegetable oil with the smashed garlic, using a fork to help release the garlic flavor into the oil. Season the garlic mixture with salt, and pepper, to taste. Let sit for at least 15 minutes.
Meanwhile, prep the chicken breasts. Rinse and dry the chicken thoroughly. Find the ridge along the side of the chicken breast, and carefully pull off the tender. Take each breast and pound gently to an even thickness. Do not pound too thin; the breast will not be completely uniform. If there is a skinny little triangular tip, go ahead and cut off and discard. Prep the tenders by slicing off any jagged edges. Liberally salt and pepper the chicken and allow to sit at room temperature for at least 15 minutes.
Preheat the grill to hot.
Once the chicken has rested, brush liberally with the garlic-infused vegetable oil. Place the chicken breasts on the hot grill, with the thicker portion facing the hotter part of your grill (usually the back). Allow the chicken breasts to cook undisturbed until char marks are made, about 4 minutes. Flip the chicken, keeping the thick part of the chicken toward the hot part of the flame, and cook until an instant-read thermometer inserted in the chicken reads 155 degrees F, about 3 more minutes. Place the chicken tenders on the grill and cook for 3 to 4 minutes total, turning halfway through. Allow the grilled chicken to rest for 5 minutes, covered, before serving.
Serve with Roasted Onion Tomato and Onion Dipping Sauce, if using.
Preheat the oven to 275 degrees F.
Place the halved tomatoes, onions, and garlic cloves on a baking sheet. Drizzle with half the olive oil and sprinkle with thyme, salt and pepper. Toss to coat well. Place the tomatoes cut-side down, and cook for 2 hours turning the tomatoes after 1 hour. After the second hour, remove the baking sheet, and set aside the unpeeled garlic. Place the rest of the vegetables and the pan juices in a food processor or blender. Add a tablespoon or two of water to the pan to scrape up any bits of flavor stuck onto the baking sheet and add to the food processor. Squeeze out the soft flesh of the roasted garlic into the food processor and add the remaining olive oil. Pulse the mixture until chunky, or puree until smooth, depending on desired consistency. Taste the sauce and season with salt, and pepper, if necessary.
Yield: about 1 1/4 cups
*Cook's Note: The tomatoes do not have to be "good" tomatoes.