For the toasts: Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F.
Arrange the bread slices in a single layer on a baking sheet and drizzle with olive oil. Bake until light golden, about 10 minutes. Cool for 2 minutes. Rub the warm toasts with the cut side of the garlic. Set aside.
For the topping: In a medium skillet, heat 3 tablespoons of oil over medium-high heat. Add the shallots and garlic and cook, stirring frequently, until soft, about 2 minutes. Season the shrimp with salt and pepper, to taste, and add them to the skillet. Cook until the shrimp are pink and cooked through about 3 to 4 minutes. Remove the shrimp and chop into 1/2-inch pieces. Set aside.
In the same skillet, add the tomatoes and season with salt and pepper, to taste. Cook over medium-high heat until the tomatoes start to soften, about 4 minutes. Turn the heat to high. Add the wine and scrape up the brown bits that cling to the bottom of the pan with a wooden spoon. Cook for 2 minutes. Stir in the stock and cook until most of the liquid has evaporated, about 2 minutes. Remove the pan from the heat and add the tarragon, arugula, mascarpone cheese, and chopped shrimp. Stir until the mixture is creamy. Season with salt and pepper, to taste. Arrange the toasts on serving plates and drizzle with the sauce. Sprinkle with salt and pepper before serving.