Preheat oven to 220ºC. Season the rib eye cutlets with salt and pepper, then drizzle with half the extra virgin olive oil. Set aside for 15 minutes.
Cut the carrots into quarters lengthways, then steam until tender. Meanwhile, combine the butter, honey, vinegar and spices in a saucepan then boil until syrupy. Toss with the carrots, arrange on a lined tray, then bake for 20 minutes, until glazed. Scatter with thyme.
Drizzle the broccolini with the remaining olive oil and season with salt, then scatter with lemon zest and garlic. Grill for 3 minutes, turning several times, drizzling with lemon juice from time to time. Scatter with parsley.
Cook the rib eye cutlets on a hot barbecue grill for 10 minutes, turning often, until medium. Rest for 2 minutes, then serve with the carrots, broccolini, sauerkraut and Café de Paris butter.
For the Café de Paris butter: Combine everything except the butter in a bowl, stir well and set aside for 30 minutes.
Place the butter in a mixer bowl and whip on high speed until light and creamy. Then add the marinade, one tablespoon at a time with the mixer running, until smooth. Form into logs in sheets of freezer plastic and refrigerate until firm.