Melt 2 tablespoons of the butter in a medium saucepan over medium heat; add the scallion whites and cook, stirring occasionally, until soft and translucent, about 3 minutes. Add 1 1/2 cups water, the rice, 1/2 teaspoon salt and the bay leaf, increase the heat to medium high and bring to a simmer. Stir a few times, cover, reduce the heat to low and simmer until the rice is tender and the water is absorbed, about 17 minutes. Remove from the heat and set aside.
Meanwhile, zest the lemon into a large mixing bowl and add the remaining 4 tablespoons butter, the hot sauce and a pinch of salt. Stir until well combined. Gently stir in half of the parsley, reserving the remaining parsley for garnish. Cut the zested lemon into wedges and reserve.
Sprinkle the shrimp liberally with salt and pepper. Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat. Add the tomatoes and some salt and cook, shaking the skillet frequently, until the tomatoes just start to pop, about 5 minutes. Transfer to the mixing bowl with the butter. Heat the remaining 1 tablespoon olive oil in the skillet. Add the shrimp and cook until the bottoms turn pink, about 1 1/2 minutes; flip and cook until just cooked through, about 1 minute more. Add the shrimp to the tomatoes and toss gently to coat everything with the butter and mush the tomatoes a bit more.
Fluff the rice and stir in the scallion greens. Divide the rice among 4 dinner plates, top with the shrimp, tomatoes and sauce, scatter the remaining parsley leaves over the top and put a lemon wedge on each plate. Serve immediately, with extra hot sauce.
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