Heat a large, wide, deep saucepan over medium-high heat. Coat the bottom with a thin layer of oil. Add the shrimp heads and cook, stirring occasionally, until browned. Add the onion, fennel bulb, celery, shallots, garlic, fennel seeds, star anise, and saffron. Sweat, stirring occasionally, until the vegetables are soft but not browned. Deglaze with the brandy, stirring until the liquid has evaporated. Add the Pernod and cook until the liquid has evaporated.
Stir in the butter and tomato paste and cook, stirring, for 2 minutes. Add 2 quarts water to cover, heat to a simmer, and simmer for 30 minutes. Remove from the heat, add the tarragon and parsley, and let stand for 15 minutes.
Pass the mixture through a food mill, then press through a fine-mesh sieve. Weigh the strained mixture and calculate 0.2% of the total weight. That’s the amount of xanthan gum you’ll need. Cool the shrimp liquid, then stir in the xanthan gum.
Puree with an immersion blender. Transfer to a saucepan and heat over medium heat until barely bubbling. Keep hot. Use the sauce immediately, refrigerate for up to 2 days, or freeze for up to 2 months.