First make your quick pickles of purple shallots and purple/red cabbage as the longer you leave the pickles the better: slice the purple shallots and shred the purple cabbage and place each ingredient in a separate glass jar or container; in a bowl, combine the juice of the limes, cider vinegar, salt, pepper, and sugar, stir well until the sugar has dissolved, and divide between the jars of shallots and cabbage; press the vegetables down, and top the jars up with vinegar if needed to ensure they’re covered, then refrigerate.
To poach the chicken, place in a saucepan or pot with a lid. Add the chicken and cover with room temperature water.
At this stage you can add aromatics if you want – such as garlic, bay leaves and peppercorns – but as this chicken is going into a spicy sauce we'll just add a little salt.
Bring the water to a boil and then reduce to a low simmer. Cover with the lid and check at around 8 minutes. The best way to check for doneness is to use an instant-read thermometer in the thickest part of the breast. When this measure 74°C, the chicken is done.
Transfer the poached chicken to a cutting board, allow to cool, then shred into bite-sized pieces.
In a saucepan add all the tinga sauce ingredients and bring to a boil and then simmer for 45 minutes. Add extra liquid (water or chicken stock) to end up with a reduced sauce.
While the chicken tinga is cooking, grill the corn cob: husk the corn cob, brush it lightly with a teaspoon of soft butter or olive oil, season with a pinch of salt, and place it on a hot dry griddle pan; use tongs to turn the cob every couple of minutes, so you get nice black char marks, for about 8-10 minutes or so, or until done to your liking. Transfer to a cutting board to cool a little, then stand the corn up, holding the top of the corn with one hand, and with the other use a sharp knife to slice the kernels off the cob.
Warm the soft flour tortillas over the dry griddle pan, then transfer them to plates and assemble your tacos: divide the chicken tinga and corn between the tacos, and garnish with the pickled purple shallots and purple cabbage, crumbly cotija cheese, and coriander.
Serve with dishes of pickles, cotija cheese, lime quarters, coriander, and Mexican hot sauces.