Make the dressing: In the bowl of a food processor, combine the egg yolk, mustard, garlic and 1/2 teaspoon each salt and pepper. Pulse to blend. With the machine running, pour the lemon juice and caper brine into the mix. Slowly pour in the olive oil, then the canola oil, blending until smooth. Transfer the dressing to a bowl and taste for seasoning. Stir in the anchovies and anchovy oil. Cover and refrigerate until ready to use, or up to 1 day.
Prepare the salad: Cook the bacon in a small skillet over low heat, stirring, until crispy, 12 to 15 minutes. Drain on paper towels.
Heat 1 inch canola oil in a medium heavy-bottomed pot until a deep-fry thermometer registers 350 degrees F (or alternatively, use a deep fryer). Line a baking sheet with paper towels. Put the capers in a small metal strainer, submerge them in the hot oil and fry until crispy, 1 to 2 minutes. Drain on the paper towels. Add the Brussels sprout leaves to the hot oil in small batches (step back because they will splatter oil) and fry until crispy, 1 to 2 minutes. Transfer to the paper towels using a slotted spoon. Season the leaves with salt.
Assemble the salad: Pour about three-quarters of the dressing into a large salad bowl. Add the romaine, basil and grated parmesan and toss to coat. Shave additional parmesan over the salad. Top with the remaining dressing, the bacon, capers and Brussels sprout leaves. Serve immediately. Photograph by Kang Kim