Begin by preparing a smooth paste using anchovies and garlic. Drain the oil from the anchovy fillets and mince them together with the garlic cloves. Continue chopping and pressing the mixture with the flat side of your knife until it forms a cohesive, paste-like texture. This should take about three minutes.

Place the egg yolks into a medium-sized bowl and whisk them until they reach a silky, smooth consistency. Add the Dijon mustard and whisk again until fully incorporated, creating a uniform base for the dressing.

Next, mix in the anchovy-garlic paste. Stir thoroughly to ensure the flavors blend seamlessly. Squeeze the lemon and measure out 2 tablespoons of juice. Gradually whisk the juice into the bowl until the mixture becomes smooth and evenly combined.

Slowly drizzle the olive oil into the mixture while whisking continuously. This step is crucial for forming a thick emulsion. Once all the olive oil has been added, continue whisking for another minute to enhance the texture.

Repeat the process with the vegetable oil, pouring it in a slow, steady stream while whisking without interruption. When all the oil is incorporated, whisk for an additional minute to achieve a creamy and well-emulsified dressing.

Finally, fold in the grated Parmesan cheese and stir until fully blended. Taste the dressing and add freshly ground black pepper as desired. Serve immediately or store in the refrigerator for later use.