Remove kernels from the cob. Keep cob to make stock, or discard. Place the corn kernels in a pot and cover with vegetable broth/water (or corn stock, if using), between 2 and 2 ½ cups. Add a generous pinch of salt. Bring to a boil, reduce to a simmer, and cook for 10 minutes.
Transfer the corn kernels to a blender (high-speed is preferred), leaving any liquid behind in the pot. Puree, adding some of the water/broth as needed, until the kernels have broken down and the mixture is paste-like.
Transfer the sweet corn back to the pan and stir in with the leftover liquid. Heat oven medium-low heat, stirring occasionally, until the mixture thickens into a polenta-like texture.
Chop the sun-dried tomatoes and add to a bowl along with the garlic, basil, red pepper flakes, lemon juice, zest, salt, and pepper. If the mixture seems a bit dry, add a splash or two of olive oil.
Divide the polenta into two bowls, top with the fried eggs, and add a few spoonfuls of the relish.