I have kind of been curious about this question for a long time. The other day, I spent a little time trying to refresh my memory on what I'd looked at decades ago and once or twice since.
First of all, as you have said, you wouldn't want to only have your 2 favorite vegetables to eat for 12 months. Maybe you are an average American. So, why not look at what the average American eats each year. The USDA tells you that:
Table 13-7. Per capita consumption of major food commodities (10 page pdf)
You will find all about consumption of red meat, flour, fats, coffee, etc. etc. This is our diet. Could we ignore that and eat
entirely out of our gardens? Well maybe . . .
However, out of about 1,800 pounds of food each year (!), the average American only eats about 725 pounds of fruits and vegetables. Now, I am "rounding" for a purpose . . . and in more ways than 1

.
Of the 750 pounds, nearly 300 pounds are fruits and 425 pounds are vegetables. Of those vegetables, about 125 pounds are potatoes.
Actually, I like to think of these food groups in units of
spuds. Since "spud" isn't a real word, I use it as equal to the annual consumption of potatoes/American, 125 pounds. But, I won't confuse you with that
Anyway, and approximately, an American eats:
125 pounds of potatoes,
250 pounds of other vegetables, and
250 pounds of fruit.
You see, an American also eats:
125 pounds of red meat
125 pounds of other animal protein (including poultry, fish, eggs, & cheese)
125 pounds wheat flour
125 pounds sugar
125 pounds other foods (fats & oils, rice, nuts, etc.)
(remember, 1
spud = 125 pounds)
Then there is milk . . . but that's a liquid. So is beer . . .
Now, if you increase how many
spuds you consume of any 1 group, you can hope that the other groups will decrease. Certainly, if you increase the
spuds of potatoes, you can decrease the amount of wheat flour. I can testify to that. When I was a kid, we ate very little bread but had potatoes every day. Of course, there are people in the world who eat very little flour or potatoes but eat rice with every meal.
Anyway . . .

. . . if you are going to consume as many fruits and vegetables out of your garden as the average American eats each year, you need about 750 pounds per person.
Steve's digits