Is this Starter related?

My first question to the group. Subject is '06 330Ci ZHP with about 91k miles. Knocking on wood, it has been trouble-free so far.

In the past month and occurring about once a week, when I start my car when cold (NJ winter), there is a shudder that comes from the front that feels like the something reluctantly engaging. After this slight shudder the car starts and everything is smooth and wonderful. When the car is warmed-up there is no issue starting.

I've been sure to fully depress the clutch pedal before starting and no other symptoms exist. Looking forward to hearing your wisdom.

If it's a starter issue, you're gonna get some whining/grinding and hard starts. Shudder shouldn't be starter related at all.

how cold does it have to be to get the problem?
how warm does it have to be for the problem to not appear?

does the engine condition (warm, cold, etc.) seem to have any part in when the problem appears?

also, any CEL (check engine light) on at the moment?