For the saffron mayo: Add chicken stock and 1 cup water to a medium pot and bring to a simmer. Keep on low heat until ready to use. Poach garlic in the pot of stock and water for 5 minutes, then remove from the stock (keep the stock over low heat).
Pour 2 spoons of the hot stock over the saffron in a small bowl to bloom it. Add saffron stock, garlic cloves, mayonnaise, olive oil, Piment d'Espelette and orange zest and juice to a blender and puree until smooth. Set aside.
For the paella: Heat a paella pan over medium-high heat and add olive oil to coat. Once oil shimmers, add chorizo and squid and cook, stirring, until squid begins to brown and chorizo renders out some of the fat. Remove chorizo and squid from pan and set aside.
Reduce heat to medium and add shallots, garlic, cherry tomatoes and olives. Stir to combine and cook until shallots become translucent and tomatoes begin to burst, about 4 minutes. Add the rice and mix to coat, then cook for an additional 2 minutes. Add the white wine and bring to a boil, then reduce down to a simmer. Add the squid ink, paprika and warmed stock and mix to combine. Turn heat to medium and allow to cook, uncovered, without stirring, until you can hear some sizzling at the bottom of the pan and it starts to crisp on the bottom, for about 25 minutes. Add the chorizo and squid back to the pan and distribute evenly on top. When squid is heated through, remove paella from heat and serve right out of the pan. Serve with dollops of saffron mayo, parsley and chives.