Bring water and salt to a boil in a large saucepan; pour polenta slowly into boiling water, whisking constantly until all polenta is stirred in and there are no lumps.Reduce heat to low and simmer, whisking often, until polenta starts to thicken, about 5 minutes. Polenta mixture should still be slightly loose. Cover and cook until tender, stirring every 3-4 minutes.Remove from heat and allow to melt, mix in Parmigiano-Reggiano cheese and stir to combine.
In saute pan heat half of the olive oil in skillet over medium low heat. Add garlic and cook for 30 seconds. Add swiss chard and cook for 2-3 minutes, season with salt and pepper and stir until combined and leaves are wilted. Remove from heat and hold warm.
Using second half of oil, heat a non-stick skillet and fry two eggs. To assemble each plate portion about 1 cup polenta, top with chard (approx. 1/2 cup), and two eggs.