Cook 4 oz. thick-cut bacon, cut into ½" pieces, and 1½ tsp. extra-virgin olive oil in a medium skillet over medium heat, stirring occasionally, until bacon is browned and crisp, 8–10 minutes. Using a slotted spoon, transfer bacon to paper towels to drain. Spoon 2 Tbsp. bacon fat into a small bowl and set aside.
Place 1 lb. baby Yukon Gold potatoes, scrubbed, in a large saucepan and pour in cold water to cover; season generously with kosher salt. Bring to a boil, then reduce heat and simmer potatoes until a paring knife slides easily through the flesh, 20–25 minutes. Drain and let cool 5 minutes.
Preheat oven to 400°. Spread out potatoes on a parchment-lined baking sheet. Using the bottom of a measuring cup or a potato masher, gently smash potatoes to about ½" thick. Let cool another 5 minutes.
Drizzle reserved bacon fat and remaining 1 Tbsp. extra-virgin olive oil over potatoes; season with salt and freshly ground pepper. Roast until potatoes are golden brown and crisp, 40–50 minutes.
While the potatoes are roasting, beat 8 oz. fresh goat cheese in the bowl of a stand mixer fitted with the paddle attachment on medium speed until smooth, about 1 minute. (Or use a whisk and a large bowl.) Add 1 small shallot, finely chopped, 3 Tbsp. whole milk, and 2 Tbsp. sour cream and beat until mixture is light and fluffy, about 1 minute. Add zest and juice of 1 lemon and 1 Tbsp. finely chopped tender herbs (such as dill, chives, and/or tarragon); season with kosher salt and freshly ground pepper. Beat to combine.
Arrange potatoes on a platter or divide among plates. Top each with 1 avocado, sliced, cut into 1" pieces, whipped goat cheese, some bacon and 1 scallion, thinly sliced, a healthy spoonful of caviar from one 1.75-oz. jar salmon caviar, preferably wild and smoked, and more herbs. Drizzle with extra-virgin olive oil.
