I think you are off to a good start and this a great paragraph. However, I do not think I would use this as the introduction. This paragraph does a great job of showing the reader what "mores" means to you, but the introduction should introduce the reader to all three words. I would use this paragraph in the body, and define the other two words in a way that relates to you as well.
"Mores" is the glue that builds me up and that holds me together
I think this is a great line, but I would leave out "builds me up."
foundation of my being, my families being.
"foundation of my being, and my family's being."
when my great-great-grandparents, my grandmother, Maria, and my grandfather, Augusto
You describe them as your great-great-grandparents, but then you you say grandmother and grandfather. I would leave grandmother and grandfatehr out and simply state their namees, since you already told us their relation to you once in the sentence.
The story of my family centers greatly around the cappelletti, the dish of Modena and Forli in Northern Italy, where Augusto and Maria originated from.
The story of my family is greatly centered around cappelletti, which is a dish from Modena and Forli in Northern Italy where Augusto and Maria originated from.
I am not an expert writer, but hopefully you find this somewhat helpful.