How to Make It
Preheat the oven to 350°. On a rimmed baking sheet, toss the bread cubes with 2 tablespoons of the olive oil. Bake until golden and crisp, 8 to 10 minutes. Let cool. Leave the oven on.
Using a medium melon baller, scoop the inside of the tomatoes into a small gratin dish, leaving a 1/4-inch wall on the sides. Lightly sprinkle the inside of the tomato cups with salt and drain upside down on a paper towel–lined plate.
In a large nonstick skillet, heat 2 tablespoons of the olive oil. Add the onion and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Add the rosé and cook until almost completely evaporated, about 5 minutes. Scrape the mixture into a medium bowl and wipe out the skillet.
Heat 1 tablespoon of the olive oil in the skillet. Add the spinach and cook over moderately high heat, stirring, just until wilted; transfer to the bowl. Add the ricotta, piquillos, Parmigiano-Reggiano, basil, parsley, garlic, thyme, rosemary, olives and piment d'Espelette. Season with salt and pepper.
Set the tomatoes in the gratin dish in their juices and stuff with the ricotta filling. Bake until the tomatoes are softened, about 20 minutes. Set the tops on the tomatoes and bake for 10 minutes longer.
Using a slotted spoon, transfer the stuffed tomatoes to a plate; cover to keep warm. Transfer the cooking juices to a blender and add the remaining 1/4 cup oil; puree until smooth. Strain the sauce into a small saucepan and season with salt and pepper. Simmer over moderately low heat, stirring occasionally, until slightly thickened, about 10 minutes.
Spoon the sauce into shallow bowls and set a stuffed tomato in each one. Garnish with the croutons and arugula, drizzle with olive oil and serve.