Oops, it doesn't look like 'eleven day' is a national day..

Other days

reading

Reading Day
coffee

Coffee Day
bow tie

Bow Tie Day
cat girl

Cat Girl Day
lash

Lash Day
offer

Offer Day
promposal

Promposal Day
youth

Youth Day
eat what you want

Eat What You Want Day
pumpkin

Pumpkin Day