In a medium skillet, heat the olive oil, then add the cherry tomatoes and saute for about 1 minute. Add the basil leaves, salt, and pepper, and saute for another 30 seconds.
1 tablespoon olive oil, ½ cup cherry tomatoes, halved, handful fresh basil leaves, ¼ teaspoon salt, ¼ teaspoon pepper
Place the avocado halves cut side up on a baking sheet lined with parchment paper. Carefully spoon the tomato/basil mixture into the hole left when the pit was removed.
2 Hass avocados
Distribute the shredded cheese on top of the avocados.
½ cup shredded mozzarella cheese
Place the avocados in the oven and bake 6-8 minutes, until the cheese has melted.
While the avocado are baking, combine the vinegar, sugar, and water in a small saucepan. Bring to a boil then lower the heat to maintain a simmer.
¼ cup balsamic vinegar, ¼ cup sugar, 2 tablespoons water
Cook for about 5 minutes, until the mixture reduces by about a third. Remove from heat and let cool to room temperature.
When the avocados finish baking, drizzle with the balsamic reduction and serve immediately.
Notes
You can use halved grape tomatoes, or dice a large tomato and drain off the excess liquid prior to placing in the skillet.
There's no need to peel the avocados.
If it's difficult to get the avocado halves from leaning too much on the baking sheet, strategically shave a strip of skin from the bottom to provide a more even balance.
Provolone and gouda are also good choices for cheeses to use.
If you are short on time, skip making the balsamic reduction and just drizzle with prepared balsamic dressing.