For the avocadoes and tomatoes: Slice the avocadoes in half lengthwise. Carefully remove the pit. Using a spoon, scoop out the flesh from the skin and then dice.
In a large bowl, toss the avocadoes with the lime juice, chile paste, cilantro, garlic, and salt. Taste to make sure it is delicious and well seasoned. Cover with plastic and let sit.
Toss the cherry tomatoes with olive oil and season with salt. Taste to makes sure they are delicious. Cover and let sit.
For the corn cakes: Melt the butter in a small saucepan over low heat. Combine the cornmeal, flour, baking powder, and salt in a large bowl. Stir to combine. Make a hole in the center of the dry ingredients and add the eggs, milk, and melted butter. Stir until just combined. Add in the corn kernels and stir to combine.
Coat a cast iron pan with olive oil and bring to a medium-high heat. Spoon the batter into the pan the size of half dollars. When the sides of the cakes have set and the bottom is lightly browned, turn the cakes over and cook on the other side.
Remove the cakes and top with some avocado and a tomato half.