What is "mi'Macharas ha'Pesach"?
Rashi: It is the day we wave the Omer (Nisan 16). They offered the Omer first (before eating the grain of Eretz Yisrael).
Radak: It is the night of Nisan 15 and the following day. 'Pesach' is the day we slaughter Pesach, i.e. Nisan 14. Also "ba'Chamishah Asar
If they first ate from the grain of Eretz Yisrael on the day after Pesach, how did they fulfill the Mitzvah of Matzah?
Radak, Malbim: They ate Matzah from old grain. The new was forbidden until after offering the Omer. Avur ha'Aretz" is from Shanim (years) she'Avru. 1
Radak: The Aseh of Matzah did not override the Lav of Chadash, because it is not written b'Tzidah. They bought old grain from Nochri merchants. (This is like R. Yosi (Yerushalmi Chalah 2:1), and unlike R. Yonah. R. Shimshon (Chalah 2:1)
Why did they eat Matzos and Kaluy (parched grain)?
Radak: This was from old grain that they found. It was not enough; they needed also manna. The next day, the manna ceased; they offered the Omer, and were able to eat enough from the new grain.
Malbim: Matzos were for the Mitzvah. Kaluy was for delicacies. By the way, we learn that as long as they had manna, they did not eat grain, only for the Mitzvah and a small amount of delicacies 1 .
What is his source that they ate only a little Kaluy? Perhaps they gave to their children something they were not used to, to gladden them on the festival, or to keep them awake until it is time to eat Matzah (Pesachim 109a. - PF)