When you say 'fast' charge do you mean DC rapid and 'slow' AC?
What current can you deliver from for solar and what EVSE do you have?
I refer to the current, but yes, as AC charging is limited to 7 / 11 KWh this will be slow charging, and DC fast chargers is fast charging.
I have a Growatt system, that can deliver 3660 watt's, so i usually use it with my wall charger set to 13A (3 KWh, but only about 2.8 makes it to the car, the rest is lost to heat in the wall charger and onboard charger)
This is really "slow" charging, but seeing as i have a daily commute to work of about 10 miles each way, i can actually already now, get the battery up to 80% every day. if we do longer journeys, the car just sits on the charger in the weekend.
The solar system i have has, as said a 3660 Watt inverter, but in case there is more than 3660 watt's produced, it will also charge my 6½ KWh battery.
So, to get the most out of the solar cell's it is best to use as close to 3660 watts (including whatever the house uses) as this will slow down the battery charging. As long as the battery is charging i can make a max of 3660 watts times 2, divided between the battery and load.
The system is constructed in such a way, that a smartmeter measures the current draw on the 3 phases, combined, and then it tries to match the combined load, by delivering to the grid, the same current, but only on one phase.
The one thing i wish i had known, that i do now, is that 3600 watt inverter power is a bit low. I would have rather paid a bit more, and gotten one that could actually handle the 7200 KWh peak, that the solar panels are rated for.
This way i could have charged the car at a higher rate, AND run the wife's hobby machines (Washer, clothes dryer and dishwasher) at the same time.
Not a huge problem though, we just time these machines to do laundry and wash dishes offset from eachother when we are at work. So when we get home, they are finished, and we can dedicate all of the excess power to the car.
The only time i expect to have to charge away from home in the near future is once at a fast charger for a longer work related trip (That i am paid for every kilometer i drive, and the first many kilometers are free, because i charged the car at home for "free") oh and once or twice when going on summer holiday. (Not THAT far, we opted to stay domestic this year, the whole world situation right now seems a bit unstable so we decided to stay closer to home).