In a medium saucepan, bring the stock to a boil with 1 tsp. salt and 1/2 tsp. pepper. Add the grits and cook over medium heat, whisking constantly, until thick and creamy, about 4 minutes. Stir in the corn and cheese; cover and remove from heat.
In 2 separate shallow bowls, place the breadcrumbs and buttermilk. In a small bowl, mix the poultry seasoning with 1 1/2 tsp. salt and 1 tsp. pepper. Pat the chicken dry and season it all over with the blend. Working with 1 piece at a time, dip the chicken in the buttermilk, then coat in the breadcrumbs, pressing to adhere.
In a large skillet, heat 2 tbsp.oil over medium-high. Cook the chicken until browned and cooked through, about 5 minutes per side.
Meanwhile, in another large skillet, heat 2 tbsp. oil over medium-high. Add the mustard greens; season and cook, stirring often, until wilted, 2 to 3 minutes. In a food processor, pulse the remaining 1/2 cup oil with the greens and the garlic until almost smooth; season.
Divide the grits among bowls; top with the pesto and chicken.
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