How can I decode TLS that uses DH?

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I regularly capture and analyze exchanges involving data protection applications that use TLS with ECDHE used as the key exchange algorithm. My current task is to decode an exchange that used the cipher suite TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256.

I've read resources like https://sharkfesteurope.wireshark.org... which talk about ways to handle the decoding of DH-based TLS exchanges for a browser like Chrome or Firefox. But how can I decrypt a TLS-protected data stream from something other than a browser? I do have the private key used.

Thanks! tl