Doesn't much matter how you charge it, as long as you deliver the charge you want without overvolting it.

Say you use a CC/CV supply set for 1A and 2.5V. If the cap is fully discharged, then when charge begins, voltage will step up by ESR * 1A (not too much, short-term ESR is usually reasonably small on these; assuming they're the power kind, not the memory-backup kind), and on top of that, ramp at about 1A/10F = 0.1 V/s. So, it'll reach nominal voltage in around half a minute. Maybe shorter than this, because again, effective capacitance is lower on shorter time scales.

Once nominal voltage is reached, it sits there, and current decays gradually as charge soaks in. It should drop to, say, 100mA after some minutes, 10mA after some hours, etc.

Or if it's set to a lower charge current, more charge will be absorbed on reaching nominal voltage; the effective capacitance is higher at the slower charge rate. And obviously, by the time it reaches nominal voltage, the absorption current is at most the charging current. Basically, it's already further down the soaking curve. Which is to say it's absorbed more charge already, which is another way to say the effective capacitance is higher.

Variable capacitance probably sounds weird. Capacitors are usually introduced as a fixed quantity. It's still some total capacitance period, but you can only measure that at very slow rates (microhertz). It's one of those thermodynamics versus kinetics problems. Thermodynamics is what happens at infinite time ("thermostatics" might make more sense, but it's "dyn" because it deals with energy, go figure.) Kinetics is what happens in motion (finite time).

Think of it as an equivalent circuit of many R+Cs connected in parallel, of different time constants. The total is the rating, but each individual piece may take days to charge (large RC constant). Or a ladder network where there's some immediate C, and in parallel with that an R+C. And in parallel with that C, an R+C, and... So you can think of it as a really long low-pass filter, with no output, you're just looking at it from the input end.

Tim