To make the vinaigrette:
Toss the chopped tomatoes into a blender along with the fresh basil.
Add the chopped garlic, the brown sugar, kosher salt, and black pepper.
Pour in the lemon juice, the wine vinegar, the balsamic vinegar along with the Dijon mustard.
Process starting on low speed for about 10 seconds, then turn up to medium speed and blend until the basil and tomatoes are puréed and smooth, about 30 seconds.
Pour in the olive oil and process on medium speed for about 20 seconds, blending until the vinaigrette is smooth and creamy. Let the vinaigrette chill overnight, allowing the flavors to meld together and intensify.
To assemble the salad:
Line a platter with the lettuce leaves.
Toss the tomato wedges across the lettuce along with the pearls of mozzarella. Scatter the basil leaves and the slices of red onion over the salad.
Season with a sprinkling of kosher or sea salt and freshly cracked black pepper.
Drizzle the salad with the basil-tomato vinaigrette and toss to coat.