Combine the chicken breasts, cola, salt, garlic cloves, chili pepper, and thyme in a resealable plastic bag. Seal the plastic bag, transfer it to the refrigerator, and let the chicken marinate for at least 24 hours.
Once the chicken breasts are done marinating, remove them from the resealable plastic bag and lightly dab them dry with a clean kitchen towel. Heat some vegetable oil up in a frying pan, coat the marinated chicken breasts in flour, and cook the chicken breasts on medium heat for 15 minutes, until golden brown and cooked all the way through.
Melt the butter in a large saucepan and sweat the red onions in it until they become translucent. Add in the minced garlic, water, and cola and bring the mixture to a boil. Add in the rice and salt, let everything cook for 1 minute, and put the lid on the saucepan. Reduce the heat and let the cola rice simmer on low heat for 10 minutes.
Once it's done cooking, remove the saucepan from the heat and let everything cool for 10 minutes. Stir the chopped parsley into the cola rice and serve it alongside the cola chicken.
Preheat the oven to 350°F. Heat the cola, vegetable oil, and butter in a saucepan. Stir together the cocoa powder, sugar, and flour in a large mixing bowl, then slowly stir in the cola mixture. Add in the plain yogurt, eggs, vanilla extract, and baking powder and mix everything together with a hand mixer until a smooth batter forms.
Grease an 8 x 8-inch cake pan, line the bottom of it with parchment paper, and pour the cake batter into the pan. Transfer the cake pan to the oven and bake the chocolate cola cake at 350°F for 45 minutes.
For the cola cake glaze, combine the cola, cocoa powder, vanilla extract, and butter in a saucepan and heat the mixture on low heat. Once everything is combined, remove the mixture from the heat and mix in the powdered sugar using a hand mixer. Transfer the cola cake glaze to the refrigerator and let it chill for 15 minutes, then top the chocolate cola cake with it.