Steam or boil the cauliflower until very tender, 10-12 minutes. Drain well — then drain again. (Water is the enemy of good cauliflower mash.)
Mash with butter, cream, salt, and pepper until smooth. Cover and keep warm.
Pat the chicken dry and season with salt, pepper, and paprika.
Heat the olive oil and 2 tbsp butter in a large skillet over medium-high heat. Sear the chicken 3-4 minutes per side until golden and cooked through. Remove to a plate.
Lower the heat, add the remaining 3 tbsp butter and garlic; stir 1 minute until fragrant. Pour in the broth and scrape up the browned bits; simmer 2 minutes.
Return the chicken to the pan and toss in the garlic butter. Serve over cauliflower mash with parsley on top.