In a wooden bowl combine the sliced avocado and lime juice and mash the avocado with the back of a spoon. Add the garlic, mustard, vinegar, jalapeno and salt and combine the mixture
until creamy. Add half the olive oil and stir to incorporate.
Add the Romaine lettuce leaves and coat them completely. Add the remaining olive oil by pouring in a very patient, slow, steady stream to produce a smooth, creaminess to the salad. Add the anchovies by mixing in evenly the chopped bits. Season with freshly ground black pepper to taste.
Add the jack cheese and the grilled tortilla slices and toss the salad again to coat the greens evenly.