In a large bowl, combine the tequila, brown sugar, olive oil, garlic, oregano and salt. Add the chicken, toss to coat, cover and refrigerate for 1 hour.
In a saucepan, whisk together the egg yolks, water, malt vinegar, honey, tequila, lime juice, dry mustard, coriander, cumin and chile powder. Cook over low heat, whisking, until thickened, 5 minutes; do not boil. Transfer to a heatproof bowl. Stir in the lime zest and season with salt. Let cool to room temperature, then refrigerate.
Soak 24 bamboo skewers in water for 30 minutes. Light a grill. Transfer 1/2 cup of the mustard to a small bowl. Thread the chicken onto the top third of the skewers; grill over moderate heat, turning, until browned and almost cooked, 8 minutes. Brush the chicken with the reserved 1/2 cup of mustard and grill until glazed and cooked through. Serve the skewers with the remaining mustard.