Bnei Yissaschar explains where the Medrash sees this in the verse. He explains that on this day means even in the present day. The verse means if your read these verses in the third month even in the present day it is considered as if you came to Sinai and received the Torah. There is a custom to eat dairy food on Shavuos . L hagid B aboker Ch asdecha' , 'to tell of Your Kindness in the mornings.
Food is a necessity to the creation.
God, therefor, even using judgment must provide food, even if the individuals are undeserving. Torah, on the other hand, is a gift given to us by God. He did not have to reveal his secrets. Therefor, on Torah we bless using the name of Kindness. On Shavuos , when we commemorate the giving of the Torah, which is given through God's Kindness, we eat foods that hint to Kindness.