Heat the oven to 400 degrees F.
Toss the tomatoes into a roasting pan, drizzle with some olive oil and season with salt and pepper. Cook until the tomatoes have collapsed, about 30 minutes. Remove them from the oven and let them cool.
Drizzle the garlic with olive oil, wrap it in foil, and bake it until soft, about 30 minutes. When cool enough to handle, squeeze the soft garlic onto a cutting board. Strip the needles from the rosemary, add them to the garlic, and chop them together. Pour 1 cup olive oil into a small bowl; add the garlic and rosemary mixture and lemon juice. Season with salt and pepper and mix well. Set aside until ready to grill.
Char the outside of the pepper under the broiler or over a gas flame. Put it into a bowl and cover it with plastic wrap. When cool enough to handle, peel, seed, and chop and put it into a blender. Add the mayonnaise and chili paste; process until smooth. Taste and adjust seasoning with salt and pepper; refrigerate until ready to use. (Can be made the day before.)
Heat the grill. Remove the meat from the refrigerator about 1/2 hour before you are going to grill it. Brush it with some of the flavored olive oil and season it generously with salt and pepper. Grill the tenderloin, turning frequently, until the meat is rare or medium rare, about 8 to 10 minutes. Remove to a platter and let it rest for 5 minutes, brushing it with the flavored olive oil. Cut the beef into thin slices.
To serve, put some of the flavored mayonnaise onto a piece of focaccia toast. Top it with a thin slice of the beef and spoon on some of the roasted tomatoes. Garnish with some arugula leaves and serve.
*Cook's note: Have your butcher clean the fat and silver skin from the tenderloin and tie it.
Recipe courtesy of Tyler Florence