How to aggregate based on one label value, but preserve the other label values?

I want to take the min of a metric based on one label, but perserve the other labels so I can extract them later.

Suppose I have these metrics:

Metric{label1="1",label2="2"}  0
Metric{label1="1",label2="3"}  1
Metric{label1="2",label2="2"}  10
Metric{label1="2",label2="3"}  100

If I do

min(Metric)by(label1) 

I get the correct results:

{label1="1"} 0
{label1="2"}  10

but I lose the label2, which I would like to extract later.

Is there a way to min by label1, while still preserving label2 in the result?

What I want the output of my aggregation to be:

Metric{label1="1",label2="2"}  0
Metric{label1="2",label2="2"}  10

I think you want bottomk by(label1)(1, Metric)