Bring a large pot of salted water to a boil. Add the egg noodles and prepare them according to the package directions until they reach an al dente texture. Drain thoroughly and keep them aside for later use.
In a large skillet set over medium-high heat, melt the butter. Add the diced yellow onion and cook for 2 to 4 minutes, stirring occasionally, until the onion begins to soften.
Place the chicken pieces into the skillet with the onion. Season with chicken bouillon granules, paprika, salt, and ground black pepper. Stir until the chicken is evenly coated with the seasonings.
Once the chicken is nearly cooked through, add the frozen mixed vegetables to the skillet. Stir to combine and cook for about 5 minutes, allowing the vegetables to warm through and become tender.
Add the minced garlic and continue stirring for 30 to 45 seconds, just until fragrant. Adding the garlic at this point helps keep it from scorching while preserving its flavor.
Stir in the condensed cream of chicken soup, condensed cream of mushroom soup, and milk. Mix until the sauce is fully incorporated with the chicken and vegetables.
Reduce the heat to low and let the mixture come to a gentle simmer. Cook for a few minutes until everything is hot and the sauce has thickened slightly, then turn off the heat.
Add the cooked and drained egg noodles to the skillet. Stir well until the noodles are completely coated in the creamy chicken and vegetable sauce.
Serve hot.