Add rice to a small saucepan with a scant 1-1/3 cups water. Bring to a simmer then place a lid on top, turn the heat down to low, and simmer for 10-15 minutes or until rice is tender. Remove pan from heat then let rice sit and steam for 3 minutes before scooping and spreading out onto a large plate to cool. Once cool, measure out 2 cups then use the remaining 1/2 cup or so for another dish (or just add to this dish and slightly increase amount of Tamari/kimchi, etc.)
Add eggs and 1 teaspoon sesame oil to a small bowl then whisk to combine and set aside.
Heat a large wok over high heat. Add butter then, once melted, add shallots or green onions and stir fry until slightly tender, 1-2 minutes. Add kimchi and kimchi liquid then stir and heat through, 30 seconds, before adding kielbasa. Stir fry until mixture is mostly dry and kielbasa is golden brown, 5 minutes.
Turn heat down to medium then add rice and cauliflower rice. Mix to combine then add remaining 1 teaspoon sesame oil and go around the wok a few times with Tamari - I usually add about 1 Tablespoon. Stir fry until cauliflower rice is tender, 3-4 minutes.
Push fried rice to the sides of the wok to form a well in the center then pour the egg mixture inside. Scramble eggs then toss with the rice to combine.
Let fried rice cool for 10 minutes or so before tasting and adding additional tamari if necessary. Scoop into bowls then serve.
Notes
Swap in store-bought riced or crumbled cauliflower to make this dish come together even faster.