Combine the beet juice, vinegar, fennel seeds, thyme, star anise, fennel, and garlic in a large heavy duty bottomed pot. Bring to a boil, and reduce the heat to a simmer for 1 hour 30 minutes.
Strain the liquid into a clean pot and discard the solids. Continue reducing the liquid, straining every hour into a clean pot. The lower and slower the liquid reduces, the better it will achieve a light syrup consistency. Remove from the heat and strain one last time.
Combine the cream, creme fraiche, horseradish, shallots, garlic, and fennel in a sauce pan, and bring to a boil. Reduce to a simmer and cook for 25 minutes, then season with salt and pepper.
To serve, gently heat cream sauce until hot (not boiling), and froth with and immersion blender.
Bring a large pot of salted water to a boil and prepare an ice bath. Remove the outer leaves from the cauliflower, and then submerge the head in the water for 5 minutes. Remove the cauliflower from the water and shock in the ice bath.
When the cauliflower has cooled, slice it, then heat a sauté pan over medium heat and add the oil. When the oil is hot, add the cauliflower and cook for 5 minutes. When seared and golden brown, flip over and add the butter, and some salt and pepper. Remove from the pan and dry on paper towel.
Combine the oil and lemon zest in a small saucepan. Set over low heat, add the salmon and cook very gently in the lemon oil to infuse oil with lemon, flipping halfway through. Serve with the toasted cauliflower, horseradish cream, and beet jus - enjoy!