Begin by crushing the taralli or your alternative crackers in a food processor until they reach a fine crumb texture.
Combine the crumbs with olive oil in a bowl and mix well until the mixture binds together securely.
Firmly press this crust mixture into the base of a springform pan, ensuring it's evenly packed. Use the back of a spoon for better compression.
Refrigerate the crust for at least 30 minutes, or speed up the process by placing it in the freezer for about 15 minutes.
Cut the mozzarella into pieces and blend it until nearly smooth while retaining some texture.
Place the blended mozzarella in a colander and press out excess moisture gently. Allow it to drain for a few minutes.
In a mixing bowl, combine the drained mozzarella, ricotta, and grated Parmigiano, blending until you achieve a creamy consistency.
Once the crust has chilled, evenly spread the cheese mixture over it, smoothing it out with a spatula.
Chill the assembled cheesecake in the refrigerator for a minimum of 1 hour to allow it to set properly.
When ready, gently loosen the edges of the cheesecake from the pan using a spoon, and carefully remove the rim.
While the cheesecake is setting, rinse and dry the tomatoes. Depending on their size, slice or halve them, then sprinkle lightly with salt.
Delicately arrange the sliced tomatoes on top of the cheesecake, adding fresh basil leaves for a classic Caprese presentation.
For an added flavor boost, finish with a gentle drizzle of extra virgin olive oil before serving.