Begin by making a mayonnaise with the first 7 ingredients. In a medium bowl, whisk together the garlic, shallot, mustard, egg yolks, and sherry vinegar. Slowly whisk in the olive oil, drop by, drop. Continue by whisking in the vegetable oil, balancing the, texture with a few drops of warm water if necessary. Season the dressing with salt, pepper and lemon juice.
Crumble in the cheese and fold in the cream with a rubber spatula. The dressing should be thick and chunky. Double-check the flavor balance, adding a few drops of lemon juice, salt or pepper as needed.