Melt butter in a large pot over medium heat. Once melted, whisk in the flour and stir constantly for 1–2 minutes until smooth. Whisk in garlic powder, onion powder, salt, pepper, mustard, bouillon, and paprika. Slowly pour in the milk, whisking constantly, until slightly thickened (about 1–2 minutes). Gradually whisk in the chicken stock and bring to a boil.
Once boiling, stir in the uncooked pasta. Reduce heat to medium-low and let the mixture gently bubble. Stir often, scraping the bottom, for 7–12 minutes or until the pasta is al dente and the sauce has thickened (see note 1)
While the pasta cooks, microwave the pulled meat just until warmed (use the lowest time listed on the package). Remove any visible fat or gristle and shred any large chunks with a fork.
Once the pasta is done, take the pot off the heat and let it sit for 1 minute. Stir in the Cheddar and Gouda, one handful at a time, so the cheese melts evenly and the sauce stays smooth. Gently fold in the warmed BBQ meat. Taste and adjust the seasoning if needed. Serve right away while it's hot and creamy.
Video
Notes
Note 1: Pasta doneness: Remove the pot from heat once the pasta is al dente. Dish should still look very saucy; it’ll continue softening and absorbing liquid as the cheese melts.
Too thick? Add a splash of milk.
Too thin? Return to low heat for 1–2 minutes.
Nutrition Note: Nutritional information may vary, depending on the brand of BBQ meat used.Storage: Best right after cooking, as the sauce thickens as it sits. Store leftovers in an airtight container in the fridge for up to 3 days. Reheat on the stove with a splash of milk to refresh the sauce.