Preheat the oven to 200C/400F. Add the halved baby potatoes to a baking dish, drizzle with olive oil and toss to coat.
Whisk together the lemon juice, lemon zest, Dijon, oregano, paprika, salt, pepper, garlic powder and olive oil. Rub all over the chicken thighs. Nestle the chicken skin-side up among the potatoes and scatter the smashed garlic cloves around. Set the 2 garlic heads (drizzled with oil and salt, wrapped in foil) in the dish to roast alongside.
Roast for about 40-45 minutes, until the chicken is golden and cooked through and the potatoes are tender.
Make the garlic Parmesan butter: melt the butter with the crushed garlic, then stir in the Parmesan and black pepper. Spoon and brush it over the chicken and potatoes, shower with the 1/2 cup grated Parmesan, and return to the oven for a few minutes to melt.
Make the roasted garlic tzatziki: squeeze the soft roasted garlic cloves into a bowl and mash. Stir in the Greek yogurt, grated cucumber (squeezed dry), dill, lemon juice, olive oil and salt.
Spread the tzatziki onto plates, top with the chicken and potatoes, and garnish with parsley, dill and an extra grating of Parmesan.
Method reconstructed from the video (the written steps were pinned in the comments). From Ben Chelin on Instagram.