Step 1In a medium, heavy-bottom saucepan, heat the olive oil over medium heat until hot. Add the celery, onion, carrot and garlic, and cook, stirring frequently, until softened and lightly caramelized, about 10 minutes.
Step 2Stir in the mushrooms and continue to cook, stirring frequently, until the mushrooms have rendered their liquid and are lightly browned, about 8 minutes.
Step 3Stir in the tomato paste and continue to cook, stirring frequently, until the paste darkens slightly and forms a thin film on the bottom of the pan (careful not to burn), about 5 minutes.
Step 4Stir in the mushroom or vegetable broth, scraping the flavoring from the bottom of the pan, then stir in the tarragon and bay leaf. Continue to cook, stirring frequently, until the mixture is reduced to a thick, sauce-like consistency, 3 to 5 minutes. Season with one-half teaspoon salt and one-fourth teaspoon pepper, or to taste.
Step 5Remove from heat and discard the tarragon and bay leaf. This makes about 2 cups of sauce. Reserve the sauce in a warm place, or cover and refrigerate until needed, warming on the stove top and thinning as needed with additional broth before serving.
Step 1Bring a large pot of water to a simmer, or prepare a large steamer.
Step 2Place 2 pieces of eggplant each in a large vacuum-seal bag or sealable plastic bag. Sprinkle a pinch each of salt and pepper over the eggplant pieces in each bag, then drizzle over the olive oil (2 tablespoons plus 1 teaspoon in each bag). Divide the lemon zest, thyme and sage between the bags, then seal, removing as much air as possible.
Step 3Place the bags in the simmering water (you will need to weigh them down with a plate or small pan to keep them submerged) or in the steamer basket. Cook the eggplant until softened and tender, 12 to 17 minutes in simmering water and up to 30 minutes steamed.
Step 4Remove the bags and place them in an ice bath to stop the cooking process. The eggplant can either be held at room temperature if cooking right away (keep sealed in the plastic bags) or can be prepared ahead of time and refrigerated up to one day until needed (bring to room temperature before using).
Step 1In a medium, heavy-bottom saucepan, bring the milk and broth to a boil. Rain in the polenta and cook over low heat until softened and tender, 15 to 20 minutes, stirring frequently. Remove from heat.
Step 2Stir in the butter and Grana Padano, thin if desired with additional milk or broth, and season to taste with salt and pepper.
Step 1Stir together 2 tablespoons olive oil and the lemon zest. Set aside to infuse the olive oil with flavor while you prepare the remainder of the dish.
Step 2Remove the eggplant from the plastic bags (discard the herbs and peel), lightly patting the eggplant to remove excess moisture. Heat a large saute pan over medium-high heat until hot. Add the remaining olive oil, then add the eggplant pieces. Sear them on one side until golden-brown, 3 to 4 minutes, then flip. Add the hearts of palm to the pan.
Step 3Sear the other side of the eggplant, turning the hearts of palm as needed until seared on all sides, about 2 minutes. Shortly before the eggplant and hearts of palm are done, add the broccolini to the pan, tossing with the oil and warming.
Step 4Remove the eggplant, hearts of palm and broccolini from heat. Cut a round out of the center of each piece of eggplant using a knife or very small cookie cutter. Fit a piece of heart of palm in each hole to mimic the bone in osso buco.
Step 5To plate, place a spoonful of polenta in the center of each of 4 dishes. Top with the "osso buco." Top with a spoonful of mushroom Bolognese. Divide the broccolini among each serving. Garnish each serving with a drizzle of lemon-infused olive oil and lemon zest. Serve immediately.