The great sage Hillel was a culinary genius

We all know that Hillel took some roast lamb and horseradish and made a sandwich from that and matzah. What I've just learned today is that it tastes really good.

I took some matzah and broke it into bite-sized pieces. On each I placed a sliced bit of hot lamb, and dolloped a generous portion of ground horseradish [ours isn't very strong this year] on top. A leaf of parsley on top made a nice garnish.

Tasty, and could be reasonably served to guests.

While I was doing this, I got to thinking about how unwieldy matzah is due to its tendency to break. I was wondering if Hillel had to put up with this problem when making his sandwich. Does matzah have to be crispty like an oversized saltine? Could you make a flat bread which is kosher for Passover but which retains a bit of flexibility and resiliency, say like a pita? Maybe if you made it the day before and wrapped it so it didn't have to sit around for a long time? Because a matzah like that would be a lot easier to work with in a meal.