Preheat oven to 400 degrees Fahrenheit and grease a medium skillet. Set aside.
Next, add butter to a medium pot on medium-high heat and once butter melts, add mixed vegetables and onions. Add sea salt + black pepper, to taste. Toss and cook vegetables until softened, about 5-6 minutes.
Add flour to veggies, stirring until well incorporated and cooking everything for 1 minute or so, until fully coated. Add in white cooking wine, chicken stock and milk. **NOTE: Be sure to whisk in the liquid with the vegetables as soon as it's poured in to ensure that NO lumps are formed.**
Once well incorporated, increase the heat to high heat so that the mixture begins to boil for about 3-4 minutes, then reduce to a simmer. Finally, add in the shredded chicken, tossing it in to ensure that it's well incorporated and then simmer until sauce thickens, about 5-6 minutes.
Once thickened, turn off the heat and stir in shredded cheeses, until fully melted and creamy. Set aside.