Making mozzarella: In a large pot, bring 2 quarts water and the kosher salt to a boil. Remove from heat and let cool to 180 degrees F.
Add mozzarella curd to a large bowl and bring to room temperature. When the water has cooled to 180 degrees F, ladle it onto the curd. The curd will begin to look like shaggy mozzarella. Using a wooden spoon, stir and stretch the cheese until it forms a cohesive ball and takes on a "plastic" texture.
Shaping mozzarella: Place half of the whey water (the salted water that turned the cheese curd into mozzarella) in another large bowl and chill to 80 degrees F. Meanwhile, work the mozzarella that's in the remaining warm whey water into 1 large ball. Knead and stretch the ball of cheese until there are no more lumps. Once the cheese is smooth, pull off a 4-inch section and put it into the second bowl containing the cooled whey water. Repeat this process with the remaining cheese.
Making stracciatella: Take each of the sections of the mozzarella out of the cooled water and pull apart the strands (like string cheese). Put all of the pulled strands of cheese into a mixing bowl and add the heavy cream. Gently stir to make stracciatella. Set aside.
Preheat oven to 400 degrees F. Place baguette slices on a baking sheet. Drizzle olive oil over the slices and place in the oven to toast, about 10 minutes. Remove from oven and, while still warm, rub cut side of garlic over the toasted bread. Then rub the bread with the cut side of tomato while gently squeezing the tomato halves. Top slices with a generous spoonful of stracciatella followed by a drizzle of olive oil, flaky sea salt and freshly cracked black pepper.