Wash carrots. Peel, wash again, slice and set aside.
Regular pot: Heat oil, sauté fennel in the pot till translucent. Add prepared carrots and 1 litre (4 cups / 32 oz of vegetable broth). Simmer under carrots are quite soft -- about 30 minutes. OR
Pressure cooker: Heat oil, sauté fennel in the pot till translucent. Add prepared carrots and 1 litre (4 cups / 32 oz of vegetable broth). Cook on high pressure for 15 minutes. (Use a pressure cooker at least 8 litres (quarts) in capacity. If you double the recipe, you'll either need to do this step in two rounds, or have a much bigger pressure cooker such as a Presto or All-American 16 quart pressure canner.)
Let the mixture cool a bit until it is safe to work with.
Purée in blender.
Put mixture back in pot.
Add the remaining 2 litres (8 cups / 64 oz ) of stock.
Bring back to a boil, simmer on low for 20 to 30 minutes.
Adjust flavouring with some or all of the suggested flavourings above.
Put into jars.
Leave 3 cm (1 inch) headspace, regardless of jar size.
Wipe rims, apply lids, set in pressure canner.
Process pressure: 10 lbs (69 kPa) weighted gauge, 11 lbs (76 kpa) dial gauge (adjust pressure for your altitude when over 300 metres / 1000 feet.)
Process time: Half-litres (pints) 40 minutes; litres (quarts) 50 minutes