Put the rinsed sushi rice and 2 1/2 cups water into a medium saucepan. Bring to a gentle boil, then cover, reduce heat to low and simmer 15 minutes. Remove from heat and let rest, covered, for 10 minutes.
While the rice rests, whisk together 3 tablespoons rice vinegar, 2 tablespoons sugar, 1 teaspoon salt and the mirin (if using) in a small bowl until the sugar dissolves. Pour the seasoning over the hot rice and fold with a wooden spatula using a cutting motion to avoid smashing the grains. Spread rice into a shallow dish to cool slightly while you prep toppings (about 5–8 minutes).
Make the dressing by stirring 3 Tbsp soy sauce, 1 Tbsp rice vinegar, 1 Tbsp toasted sesame oil, 1 Tbsp honey and the lime zest in a small bowl. In a separate small bowl combine mayonnaise and sriracha to make spicy mayo; taste and adjust heat.
If you prefer lightly seared salmon: toss the cubed salmon with 1 tablespoon soy sauce and 1/2 teaspoon toasted sesame oil and let sit 8–10 minutes. Heat a nonstick skillet over medium-high heat, add a teaspoon of neutral oil, then sear the cubes 60–90 seconds per side until just colored at the edges but still glossy inside. Remove and cool slightly. (Alternatively, skip the sear and use sushi-grade raw salmon kept chilled.)
Arrange warm seasoned rice into four bowls. Top each bowl with equal portions of salmon, edamame, cucumber, carrot, avocado slices and scallions.
Drizzle a little soy-sesame dressing over each bowl and add a spoonful of spicy mayo in a zigzag. Scatter toasted sesame seeds and nori strips on top, and finish with pickled ginger on the side.
Serve immediately so avocado stays fresh and rice is still slightly warm. Leftovers can be kept chilled; if storing make sauce separately to avoid soggy rice.