Using a butter knife, gently split the lotus seeds in half through the top opening. Remove and discard the bitter green center. (Or buy lotus seed halves and skip this step.) Rinse under running water, place in a bowl, and cover with fresh water. Soak overnight.
The next day, drain the lotus seeds and rinse them again. In a pot, add the soaked seeds along with 4 cups (950 ml) of water. The water level should be above the lotus seeds, so make sure you're not using a pot that is too shallow or wide.
Turn on the heat, and bring the mixture to a boil. Once boiling, turn the heat down to low. Simmer the seeds for 30 minutes. The seeds are done once they’re soft, but still maintain their shape. Cool completely, and drain.
In a food processor, puree the cooked lotus seeds until smooth (it’s best to do this in two batches). Transfer the purée to a non-stick pan, cast-iron pan, or thick-bottomed Dutch oven (to avoid sticking/burning).
Place over medium low heat, and constantly stir the purée using a rubber spatula, for 30 minutes. While stirring, add the powdered sugar and oil in 3 alternating batches spaced 5-10 minutes apart, starting with the sugar. With each batch, make sure the sugar and oil is well incorporated before adding more. The lotus paste is done once it can hold its shape. It will be slightly firm, but also soft.
Cool completely, and store in the refrigerator in an airtight container. This lotus paste can be made one day in advance; it is easier to work with after it’s been chilled.