In a mortar and pestle, crush the thyme, and garlic. Mix the thyme, garlic, orange juice, white wine, and olive oil in a bowl, and let the flavors blend for 1 hour before use.
In a bowl, pour the marinade over the pieces of the portioned beef heart. Cover the bowl with plastic wrap, and place in the refrigerator to marinate for 2 hours, then remove the hearts from the marinade (discard the marinade).
Preheat a grill or grill pan over medium-high heat and lightly grease with oil.
Season the hearts with salt, and pepper. Grill the hearts to medium-rare, about 3 minutes on each side, depending on thickness.
To serve, divide the beets among 8 warm salad plates or transfer to one large warm serving platter, and top with thinly sliced beef heart, chive batons, and picked parsley dressed in horseradish vinaigrette. For garnish: grate fresh horseradish over the heart and drizzle a bit of extra-virgin olive oil.
In a mixing bowl, combine the horseradish, vinegar, orange juice, salt, and pepper, in a bowl.
Add the pure olive oil in a thin stream, whisking while pouring, to emulsify the vinaigrette.
Finish with extra-virgin olive oil. Adjust the seasoning, to taste.
Preheat the oven to 325 degrees F.
Place the baby beets, garlic, thyme, and parsley in a non-reactive roasting pan. Add the orange juice, water, and extra-virgin olive oil, making sure to coat evenly. Season the beets with fennel seeds, salt, and pepper.
Place in the oven covered with aluminum foil, and bake until the beets are knife tender, about 45 minutes. Similar to a cake, insert a knife, and if it slides in and out easily its finished.
Remove the pan from the oven, and remove the foil, being careful with the steam, and let cool. Remove the skins by taking an old dish towel and rubbing the skins off gently to keep the shape of the beets. Cut the beets into different shapes - rounds and quarters and place in a mixing bowl, then toss with salt, pepper, and the horseradish vinaigrette. Just before serving, add the chive batons, and picked parsley, and place on either individual plates or one platter, topped with the sliced beef heart and freshly grated horseradish.