1. Place the potatoes in a large pot of cold and salted water. Bring to a boil then reduce heat and simmer until the potatoes are fork tender, about 20 minutes.
2. Drain the potatoes and transfer to a large bowl to cool.
3. While the potatoes are cooking, preheat your oven to a high broil. Place the red peppers on a sheet pan and cook for 15-20 minutes, turning every few minutes to ensure all of the sides become charred.
4. Once the skin is black, remove the peppers from the oven and into a bowl and cover with saran wrap. Cover for 10 minutes and once cooled remove the skin, seeds and innards with your hands. Roughly chop the peppers and set aside.
5. To make the vinaigrette, use the back of your knife to break the anchovies into a paste. Add them to a bowl with the Dijon mustard and lemon juice. Whisk until the ingredients are well incorporated.
6. Slowly stream in the olive oil until the vinaigrette comes together and finish with the parsley, slat and pepper.
7. Combine the potatoes, red peppers and a few tablespoons of the vinaigrette and gently toss with a rubber spatula. Add more salt to taste if necessary and enjoy!