2 large egg yolks
Sugar, for caramelizing (optional)
To a large skillet, add the fennel, butter, sugar, salt, and 2/3 cup water. Bring to a simmer on medium and cover partially with a lid. Cook until the fennel has softened, about 10 minutes. Remove the lid and increase the heat to medium high. Cook, stirring often, until the water has evaporated and the butter and sugar have turned golden-brown, about 20 minutes. Transfer the fennel to a plate to cool.
In a large saucepan, combine the milk, rice, brown sugar, and salt. Bring the mixture to a boil over medium-high heat, stirring often with a wooden spoon to keep the rice from sticking to the bottom of the pot. Immediately decrease the heat to medium to maintain a low simmer and cook, stirring occasionally, until the rice is tender, 15 to 20 minutes. Remove from the heat.
Whisk the egg yolks in a medium bowl. Add about 1/2 cup of the hot milk mixture to the yolks while whisking. Repeat this process until most of the hot milk mixture is in the bowl. Pour the yolk mixture back into the pot and set it over low heat. Cook, stirring, until the pudding has thickened slightly, about 1 minute. Pour the pudding into to a clean bowl. Let the pudding cool slightly; it will thicken up a little more as it sits.
To serve, either top individual servings of the pudding with the candied fennel or stir the fennel into the pudding, top with 2 teaspoons sugar each, and use a mini blowtorch to caramelize the tops, if desired.
Serve warm or cover and chill until ready to serve. Keep leftovers in an airtight container in the fridge for up to 3 days.