1 1/2 cups converted long-grain rice
4 teaspoons kosher salt, divided
1/3 cup extra-virgin olive oil
1/2 cup plus 2 tablespoons minced parsley
1/4 cup plus 1 tablespoon freshly squeezed lemon juice
1/4 teaspoon ground allspice
3 ripe plum tomatoes, halved lengthwise, seeds squeezed out, and finely diced
1 Kirby cucumber, peeled, seeded, and finely diced
Freshly ground black pepper
Hot sauce