What are the trinity in French cooking?
Mirepoix (cuisine)
Similar flavour bases include the Italian soffritto, the Spanish sofrito, refogado/sufrito (braised onions, garlic and tomato) from Portuguese-speaking nations, the German suppengrün (leeks, carrots and celeriac), the Polish włoszczyzna (leeks, carrots, celery root and parsley root), the US Cajun / Creole holy trinity (onions, celery and bell peppers), and possibly the French duxelles (mushrooms and often onion or shallot and herbs, reduced to a paste).
American cuisine
Cajun French is more closely related to dialects spoken in Northern Maine, New Brunswick, and to a lesser degree Haiti than anything spoken in modern France, and likewise their terminology, methodology, and culture concerning food is much more closely related to the styles of these former French colonies even today. Unlike other areas of the South, Cajuns were and still are largely Catholics and thus much of what they eat is seasonal; for example pork is an important component of the Cajun "boucherie" (a large community event where the hog is butchered, prepared with a fiery spice mix, and eaten snout to tail) but it is never consumed in the five weeks of Lent, when such would be forbidden. Cajun cuisine tends to focus on what is locally available, historically because Cajuns were often poor, illiterate, independent farmers and not plantation owners but today it is because such is deeply imbedded in local culture. Boudin is a type of sausage found only in this area of the country, and it is often by far more spicy than anything found in France or Belgium. Chaudin is unique to the area, and the method of cooking is comparable to the Scottish dish haggis: the stuffing includes onions, rice, bell peppers, spices, and pork sewn up in the stomach of a pig, and served in slices piping hot. Crayfish are a staple of the Cajun grandmother's cookpot, as they are abundant in the bayous of Southern Louisiana and a main source of livelihood, as are blue crabs, shrimp, corn on the cob, and red potatoes, since these are the basic ingredients of the Louisiana crawfish boil.
New Orleans has been the capital of Creole culture since before Louisiana was a state; this culture is that of the colonial French and Spanish that evolved in the city of New Orleans, which was and still is quite distinct from the rural culture of Cajuns and dovetails with what would have been eaten in antebellum Louisiana plantation culture long ago. Cooking to impress and show one's wealth was a staple of Creole culture, which often mixed French, Spanish, Italian, German, African, Caribbean and Native American cooking methods, producing rich dishes like oysters bienville, pompano en papillote, and even the muffaletta sandwich. However, Louisiana Creole cuisine tends to diverge from the original ideas brought to the region in ingredients: profiteroles, for example, use a near identical choux pastry to that which is found in modern Paris but often use vanilla or chocolate ice cream rather than custard as the filling, pralines nearly always use pecan and not almonds, and bananas foster came about when New Orleans was a key port for the import of bananas from the Caribbean Sea. Gumbos tend to be thickened with okra, or the leaves of the sassafrass tree. Andouille is often used, but not the andouille currently known in France, since French andouille uses tripe whereas Louisiana andouille is made from a Boston butt, usually inflected with pepper flakes, and smoked for hours over pecan wood. Other ingredients that are native to Louisiana and not found in the cuisine of modern France would include rice, which has been a staple of both Creole and Cajun cooking for generations, and sugarcane, which has been grown in Louisiana since the early 1800s.
Ground cayenne pepper is a key spice of the region, as is the meat of the American alligator, something settlers learned from the Choctaws and Houma. The maypop plant has been a favorite of Southerners for 350 years; it gives its name to the Ocoee River in Tennessee, a legacy of the Cherokees, and in Southern Louisiana it is known as liane de grenade, indicating its consumption by Cajuns. It is a close relative of the commercial passionfruit, similar in size, and is a common plant growing in gardens all over the South as a source of fresh summertime fruit.