Pour the chicken or vegetable stock into a stock pot and put over a burner on medium high heat. Bring to a boil, then reduce to a simmer. Add the frozen peas to the stock along with a pinch of salt and cook until bright green in color and tender (about 2 minutes.) Remove the peas from the stock (reserving 1/2 cup for the purée, if needed) and place them in an ice bath or a tub of cold water and let them cool off for 5 minutes, until they're at least room temperature.
Pour the peas into a blender. Add the heavy cream, olive and a generous pinch of kosher salt. Blend until smooth. If the purée is too thick for your liking, feel free to add more stock, 1 tablespoon at a time, until the purée reaches a consistency of your liking.
Pour the purée into a fine mesh strainer and strain out the pea skins.
With a large spoon, dollop pea purée onto the center of a plate. Use the back of the spoon to smear it into a large circle that covers the inner three quarters of the plate. Top with the chopped cherry tomatoes. If doing this ahead, cover the plates with foil and place in the fridge. Remove them from the fridge before you make your scallops, so that the plate doesn't feel super cold when you serve it to your guest!
Dry the scallops off with a paper towel. Season generously with kosher salt on both sides.
Heat a cast iron skillet or stainless steel skillet over high heat. IF USING STAINLESS STEEL, TRY THIS HEAT TEST TO PREVENT THEM FROM STICKING! After 1-2 minutes, test if the skillet is hot enough by splashing a little bit of water onto the surface. If the water evaporates and bubbles, the skillet is not hot enough. If the water beads up and bounces on the surface, your skillet is good to go! Pour the water out of the skillet into the sink. Season the skillet with 2-3 tbsp of avocado oil. It should be shimmering immediately and start lightly smoking because our pan is so hot! Immediately place the scallops around the rim of the pan. Do not touch the scallops for 2 minutes, until golden brown. When you see a strong golden brown ring forming around the scallop, lightly lift one of the scallops (preferably the smallest one -- this is going to be your sacrificial scallop, god forbid you lift it too early) with a spatula to see if it's perfectly golden brown. If it's not there yet, put it back down and continue to let the scallops cook for another minute or so. Do not lift the scallop if the golden brown rim is only faint golden brown or light golden in color. The ring should be strong and very apparent.
Once the scallops are golden brown to perfection, flip them. Adjust the heat to medium and let them sear another minute. Move the scallops to one side of the pan.Add 3 tbsp of cold butter to the pan and let it melt. Add the lemon juice to the melted. Use a spoon to baste the scallops in the lemon butter for a minute.
Plate in a line on the the pea purée plates. Drizzle extra lemon brown butter on top and serve immediately!