Two important books for sketching out a notion of what convivial practice might entail:
The Practice of Everyday Life Volume 2: Living & Cooking - Michel de Certeau, Luce Giard, and Pierre Mayol
Culinary Artistry - Andrew Dornenburg and Karen Page
The latter book is one of the most thoughtful discussions of cooking to be found in a non-academic press publication. It begins with a discussion of whether cooking is a trade, a craft, or an art. The book uses a rather dated idea of what "art" is, but it is still useful. Culinary Artistry treats cooking as an artistic practice - from providing palettes of flavors, theories of menu construction, flavor composition, and the process of composing a dish. There are times that more rigor and a more sophisticated understanding of what contemporary art practices actually are would be nice, but given its popular press ambitions, this is not really its responsibility.
The Practice of Everyday Life Volume 2 proves a nice theoretical companion to Dornenburg and Page's book. Its second half, "Doing-Cooking" investigates a variety of culinary practices. The book is a "practical" extension of de Certeau's Practice of Everyday Life Vol 1. in which he offers ways to think about ordinary and everyday practices as moments of creative resistance and engagement. Cooking, in the second volume, serves as an example of the "...creative cunning in the undefined whirlwind of everyday practices..." What I am calling convivial practice is really just a broadened application of Giard's "doing-cooking." It is the terrain that LeisureArts seeks to operate within. We cook because it is a practice that is intricately social, mundane, and a field of pleasures. To quote Giard:
"...[re:cooking] manipulating ordinary things make one use intelligence, a subtle intelligence full of nuances and strokes of genius, a light and lively intelligence that can be perceived without exhibiting itself, in short, a very ordinary intelligence."
I forgot to thank Oliver Luker for providing the impetus for me to consider this again.
And I should also direct people to Gastronomica as an exemplary synthesis of academic/popular writing with regard to the culinary arts.
For the socio-political dimension of conviviality please see Ivan Illich's Tools for Conviviality:
"I choose the term 'conviviality' to designate the opposite of industrial productivity. I intend it to mean autonomous and creative intercourse among persons with their environment...I consider conviviality to be individual freedom realized in personal interdependence and, as such, an intrinsic ethical value."