How to Make It
In a bowl, break up the beef chuck. Add the minced chiles, two-thirds of the minced garlic, 2 tablespoons of the fish sauce and a pinch of salt and gently work the seasonings into the meat. Form the meat into 16 balls, transfer to a baking sheet and refrigerate overnight.
In a food processor, combine the coarsely chopped large tomatoes with the remaining garlic and a large pinch of salt and pulse until the tomatoes are finely chopped. Strain the tomatoes through a coarse strainer into a large bowl, pressing on the solids; you should have about 3/4 cup of juice. (To make a nearly clear tomato water, let the tomato mixture drain through a fine strainer overnight.) Whisk the fresh lime juice, sugar, 1 tablespoon of the olive oil and the remaining 2 tablespoons of fish sauce into the strained tomato juice.
In a large bowl, cover the rice noodles with water and let stand for about 20 minutes. Bring a medium saucepan of salted water to a boil.
In a large skillet, heat the remaining 1 tablespoon of olive oil until shimmering. Add the seasoned meatballs and cook over moderate heat until the meatballs are browned all over and nearly cooked through, 6 to 8 minutes. Let rest for 5 minutes.
Drain the rice noodles and add them to the boiling water. Cook the noodles, stirring, until al dente, about 40 seconds. Drain the rice noodles and return them to the pan. Fill the pan with cold water. When the noodles are cool, drain them again. Lightly pat the noodles dry, then add them to the tomato dressing and toss.
Transfer the dressed rice noodles to shallow bowls and top with the meatballs. Garnish with the fresh mozzarella, grape tomatoes, cucumber sticks and Thai basil sprigs and serve.