Preheat the grill on medium-high (400°F-425°F)
Separate the asparagus into groups of five, equal thickness, spears.
Skewer each group of five asparagus using two skewers to create “rafts”. Slide the first skewer through all five spears, 3-4 cm from the bottom of each spear. Then slide the second skewer through each spear about 4 cm above the bottom skewer.
Place the asparagus rafts on a baking sheet in a row, drizzle the top of the asparagus with 2 tablespoons of olive oil, 2 tablespoons of balsamic vinegar, then sprinkle with salt and pepper (to taste). Set aside.
Place a high-heat-tolerant skillet on the grill. Heat the skillet for a minute, then add 2 tablespoons of olive oil and the tomatoes. Sprinkle with salt and pepper (to taste) and toss to combine. Close the grill lid and cook the tomatoes for 5-6 minutes.
Add asparagus rafts and grill the rafts for 3-6 minutes until charred and just tender. The thinner spears will cook quickly, and the thicker spears will take a few more minutes.
Remove the asparagus and tomatoes from the grill and arrange the asparagus rafts on a platter or individual plates. Divide the tomatoes equally across the rafts, tear the mozzarella and sprinkle evenly over the platter (or plates). Add the basil and drizzle with 3 tablespoons of the balsamic vinegar. Enjoy!