Step 1In a bowl, mix the salt, coriander, black pepper, thyme and crushed bay leaf. Set aside.
Step 2Leaving the base of the lemons intact, cut the lemons in quarters lengthwise (do not cut all the way through). Place a couple of tablespoons of the salt mixture at the bottom of a sterile 1-quart glass jar. Add the lemons, firmly pressing them into the jar and layering plenty of the salt mixture in between the lemons. Fill to the top of the jar and top with the white wine vinegar. Tightly close the jars and store in the refrigerator for 1 month, or until the lemons are soft and fully submerged in a lemony brine.
Step 1To smoke the almonds: Place 2 tablespoons of hickory chips into a stovetop smoker or on the bottom of a heavy lidded pan, covering an area about the size of your burner (if using a pan, you will also need a rack or screen that fits inside). Place a rack over the wood chips. Place the almonds on the rack; they should not be directly over the chips. Cover the pan almost entirely, leaving it slightly open so it is possible to tell when the chips begin to smoke. Heat the burner over medium-high heat just until smoke begins to escape from the opening, then tightly cover the pan. Reduce the heat to medium-low. Continue to smoke the almonds until they are fragrant and have picked up the smoke flavor, about 5 to 7 minutes (depending on the intensity of the smoke). Be careful not to oversmoke, or the almonds will taste bitter.
Step 2Meanwhile, heat the oven to 350 degrees. Place the smoked almonds on a sheet tray and toast for 6 to 8 minutes, until golden brown, being careful not to burn. (This makes more than is needed for the salad; store any extra in a tightly sealed container.) When cool, very roughly chop about one-half cup of the almonds. Set aside.
Step 3Finely chop the preserved lemons, using both the peel and flesh, and place into a mixing bowl. Add the extra virgin olive oil, honey and white wine vinegar. Whisk until emulsified. The dressing should be sharp and lemony without being overly bitter. Add salt and pepper to taste and additional vinegar if desired to brighten the flavors.
Step 4Place the escarole into a bowl and add the chopped smoked almonds. Using a mandoline or very sharp knife, very thinly slice the sunchokes (you should have about 1 1/3 cups) and add to the bowl. Add about one-fourth cup of the preserved lemon dressing to taste, being careful not to overdress the salad (less is generally more). Add salt and pepper to taste. Divide the salad among 4 plates and sprinkle Parmigiano-Reggiano over the top. Serve immediately.