Place the potatoes in a large pot and cover with cold water. Bring the water to a boil, over medium heat, then reduce heat to a simmer and add 2 tablespoons of salt. Cook until potatoes are tender, but still firm, about 10 minutes. Drain, let cool and cut each potato lengthwise into 8 slices.
Heat grill to medium-high. Brush the potatoes with the oil and season with salt and pepper. Grill until golden brown and cooked through, about 2 to 3 minutes per side. Transfer the potatoes to a platter and drizzle with the sauce, garnish with fresh cilantro or serve sauce, on the side, as a dip.
Melt the butter in a small saucepan over medium heat, add the flour and cook for 1 minute. Slowly whisk in the milk and cook until thickened, about 3 minutes. Whisk in the cheese a little at a time until smooth.
Add the jalapenos, chile de arbol and season with salt and pepper. Keep warm.
Combine all ingredients in a small bowl.
Put mayonnaise, vinegar, garlic, tomato and paprika in food processor and process until smooth; season with salt and pepper. Scrape into a bowl and stir in the parsley.