Step 1 In a large bowl, mix together the thyme, oregano and oil. Add the tomatoes and toss to combine. Heat a grill (or grill pan) over medium-high heat until hot. Grill the tomatoes until softened, about 4 to 5 minutes depending on the heat. Remove the tomatoes to a blender and pulse until smooth. Combine the softened tomatoes with the liquid smoke and mayonnaise in a large bowl and mix well to combine. Season to taste with salt. This makes about 2 cups aioli, more than is needed for the recipe; the aioli will keep, covered and refrigerated, for 1 week.