In a 1O-inch skillet, heat 1 teaspoon oil over medium heat until just warm, less than a minute. Add bacon and cook, stirring occasionally, until starting to crisp and most of the fat has rendered, about 6 minutes. Transfer to a small plate with a slotted spoon.

Add mushrooms to drippings, increase heat to medium-high, season with salt, and toss to coat. Cook undisturbed until the mushrooms start to release some of their liquid and the undersides are browned, 3 to 4 minutes. Loosen mushrooms from pan, scraping with a wooden spoon if needed, and toss. Cook until other sides are browned and mushrooms are tender, 2 to 3 minutes more. Taste one to make sure. Transfer mushrooms to plate with bacon.

Add 1 tablespoon oil to skillet, then add grains and season with salt. If skillet looks dry or there's not enough oil to coat the grains, drizzle in more oil. Saute grains undisturbed until starting to crisp, about 2 minutes. Toss grains, then cook undisturbed until they're more or less evenly toasted and light golden brown, but not dried out, about 2 minutes more. (Whole grains have their outer hull intact, which makes them pleasantly chewy, but they can dry out and get tough if overcooked.)

Add kimchi and cook until it releases some juices, about 1 minute. Continue cooking until liquid evaporates and the bottom of the pan starts to brown. Remove from heat, return mushrooms and bacon to skillet with any accumulated juices, along with the reserved kimchi juice and cilantro. Toss to combine and rewarm the mushrooms and the bacon, about 30 seconds. Spoon fried grain mixture onto a platter.

Return skillet to medium-high heat and add remaining 1 tablespoon oil. Crack eggs into pan and season with salt. Cook until browned at edges, whites are set, but yolks are still runny (or not, if that's your preference), 3 to 4 minutes. Serve grains topped with fried eggs and with sesame oil and hot sauce for seasoning, if desired.