For the stew: Heat a 10-inch cast-iron skillet over medium heat until hot, then add the olive oil, carrots, celery, and some salt and pepper and stir. Cook until the carrots begin to soften, 5 to 6 minutes. Remove the carrots and celery to a small bowl and set aside.
Add the butter and onions to the skillet with another pinch of salt. Sweat the onions until softened slightly, 2 to 3 minutes. Add the chicken bouillon and crush it, stirring to combine with a wooden spoon. Sprinkle the flour over the onions and stir well, then allow to cook for 1 minute. Whisk in the chicken broth in thirds, whisking after each addition until smooth. Whisk in the yogurt, sugar and vinegar. Season with salt and pepper to taste. Stir in the peas, cooked vegetables and chicken. Allow to simmer on low heat while you prepare the biscuits.
For the biscuits: Preheat the oven to 400 degrees F.
Crush the chicken bouillon in a small heatproof bowl and add 2 tablespoons butter. Heat in the microwave at 10-second intervals until melted. Set aside.
Whisk together the flour, baking powder, baking soda, salt and sugar in a medium bowl. Use a box grater to grate the remaining 4 tablespoons butter into the flour, then use a fork to toss the butter into the flour. Stir in the Greek yogurt to form a smooth dough. Add 2 to 3 tablespoons water if needed to make the dough come together. Knead and turn the dough a few times in the bowl to incorporate any dry bits of flour.
Lightly flour a work surface and turn the dough out of the bowl. Give it another few kneads and then shape and flatten the dough into an 8-inch circle. Cut the dough into 6 wedges.
Stir about 2 tablespoons parsley into the simmering chicken. Arrange the 6 biscuits in a loose circle atop the chicken mixture, leaving some space in between. Brush the biscuits with the melted chicken bouillon butter.
Bake until the biscuits are puffed and golden brown, 25 to 30 minutes.
Allow to cool for 5 minutes. Sprinkle with the remaining parsley before serving.
When measuring flour, spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)