Warning: I am not a linguist!
This post is essentially a long comment on French’s use of est-ce que and your exclusion of it because “it’s a whole phrase”. I think est-ce que in modern French is not a “whole phrase” anymore, at least in colloquial French, so colloquial French is an example of Indo-European language with such an interrogative particle. (In the citation bellow, Rodney ball mentions the Polish czy, which would be another example).
The difference between formal written French and spoken French are quite large, even in grammar. While est-ce que is currently part of standard French, it doesn’t sound very formal to my native ears and is discouraged in formal writings. I believe it is a relatively recent development in French, but I clearly do not analyse it instinctively as a “whole phrase”. Rodney Ball, in his (excellent) Colloquial French Grammar, section 2.2.1, says
In many ways, est-ce que has come to resemble the interrogative markers
which in a number of languages are placed before (or after) statements in
order to turn them into questions: czy in Polish, for example. If French
lacked a writing system and was being analysed for the first time, est-ce que
might well be treated as an indivisible unit: [ɛskə].
This confirms my native instinct. Otherwise, I wouldn’t have needed a linguist to notice the redundancies of my natural way to say “What is this ?” : «Qu’est-ce que c’est», literally, *“what is it that it is”. For me, «Qu’est-ce que» is just a fancy orthography for a word [kɛskə] translating the English “what”.
The same question in 18th century French would have been asked by «Qu’est-ce ?». But est-ce without a following que is no longer used in spoken French, unless you want to sound archaic and/or formal.
Obviously, given the chronology of this development, there is no way est-ce que could be cognate to similar interrogative words in any other language.