Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the peppers over direct medium heat, with the lid closed as much as possible, until blackened and blistered all over, 12 to 15 minutes, turning every 3 to 5 minutes. Place the peppers in a bowl and cover with plastic wrap. Let stand for 10 to 15 minutes. Remove the peppers from the bowl and peel away and discard the charred skins, tops, and seeds.
In a blender or food processor, mince the garlic first, and then add the roasted peppers, salt, and bread crumbs. Add the lemon juice and paprika and, with the motor running, slowly add the oil. Blend until very smooth and orangey-red in color. If the rouille is too thick, add about 1 tablespoon of water. Season to taste with more salt, if needed.
Trim the tenderloins of any surface fat and silver skin. Lightly brush with oil and season evenly with the salt and pepper. Allow to stand at room temperature for 15 to 30 minutes before grilling.
Grill the tenderloins over direct medium heat, with the lid closed as much as possible, until the outsides are evenly seared and the centers are barely pink, 15 to 20 minutes, turning about every 5 minutes. The internal temperature of the tenderloins should be 150°F when fully cooked.
Remove the pork from the grill and let rest for 3 to 5 minutes. Cut each tenderloin crosswise into thin slices. Serve warm or at room temperature with the rouille.