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A few years later...
I found no clue among Tabanidae.
But what about Asilidae?
Some Asilinae genera (i.e., Mallophora, Megaphorus, Porasilus) that deposit their eggs in a frothy or chalky-white “case,” oviposit from 32 to 729 eggs.
In: Dennis, D. S., J. K. Barnes and L. Knutson. 2013. Review and analysis of information on the biology and morphology of immature stages of robber flies (Diptera: Asilidae). Zootaxa 3673: 1–64

About Mallophora orcina:
Oviposition occurred on vegetation 1–3 m above the ground with approximately 188–323 eggs deposited in layers in a chalky-white albumin.
In: Dennis, D. S. (2015). Oviposition, Eggs, and First Instar Larvae of Mallophora orcina (Wiedemann, 1828)(Diptera: Asilidae). Proceedings of the Entomological Society of Washington, 117(3), 269-280.

A few pics of Mallophorina egg cases: here and there.

As far as I know, none of these genera occur in Europe. So???