- Make the tamarind marinade: In a sauce pan, heat olive oil over medium heat. Add onions and a pinch of salt. Sauté until onions are lightly caramelized. Add garlic and cook a few minutes more. Deglaze pan with beer, scraping the bottom of the pan to release any browned bits. Stir in tomato paste and cook a few more minutes. Add remaining ingredients and cook for 10 minutes over low heat. Add water to pan if liquid reduces too much. Remove from heat and let cool. Transfer to a blender and process until smooth, adding water if needed to reach desired consistency.
- Brine quail and eggs: Bring a medium pot of water to a boil and prepare an ice bath. Boil eggs for 3 minutes, then transfer to ice bath. Once cooled, peel eggs.
- In a saucepan over medium heat, combine beer, salt, peppercorns, thyme, garlic, bay leaves, brown sugar, star anise, and red pepper flakes with 2 cups water. Stir until salt and sugar have dissolved, then remove from heat and refrigerate until cool.
- Place quail and boiled eggs in a pan with brine liquid and half of marinade and set aside for 1½ hours. Remove and pat dry, then refrigerate for an additional hour.
- Cook the quail: Cut quail in half lengthwise and remove wings. Skewer quail half through breast, then add a quail egg to skewer, then push skewer through the leg. Use a second skewer to keep quail and egg from rotating, if necessary. Grill skewers over medium-high heat, brushing frequently with marinade. (Be careful not to let the sauce burn. Remove from heat and brush once more with marinade before serving.