3 oil-packed anchovy fillets
1 small garlic clove
⅓ cup extra-virgin olive oil
3 Tbsp. fresh lemon juice
1 Tbsp. mayonnaise
1 tsp. Dijon mustard
2 Tbsp. finely grated Parmesan, plus shaved for serving
Kosher salt, freshly ground pepper
1½ lb. mixed tomatoes, sliced, quartered, or halved
½ cup basil leaves
Purée anchovies, garlic, oil, lemon juice, mayonnaise, mustard, and 2 Tbsp. Parmesan in a blender until smooth. Season dressing with salt and pepper. (Or, finely chop anchovies and garlic and whisk together dressing in a medium bowl.)
Arrange tomatoes on a large plate; drizzle dressing over. Top with basil and shaved Parmesan; season generously with pepper.