Preheat the grill to high. Preheat the oven to 350 degrees F.
In a saucepan over medium-high heat, add 1 tablespoon olive oil and 1 tablespoon butter.
Add the onions and cook for 1 to 2 minutes until fragrant. Add the roasted garlic paste and potato. Mix well. Cook for 2 minutes, then add a splash of white wine and 2 cups chicken stock. Bring to a simmer. Cook until potato is tender, about 8 to 10 minutes.
Once tender, add the cream and lemon juice. Season the mixture with salt and pepper, to taste. Remove from the heat and allow to cool slightly.
Once cooled add the mixture to a blender. Add a bunch of chives, remaining 1 tablespoon butter, and 2 tablespoons chicken stock. Pulse until pureed and smooth.
Season the chicken chops with salt and pepper, to taste, and drizzle with the remaining olive oil. Put the chops on the hot grill and cook for 4 to 5 minutes on each side. Transfer the chops from the grill to sheet pan and bake in the oven for 6 to 8 minutes. Remove the pan from the oven and arrange the chops on a serving platter. Serve with roasted garlic and chive puree.