In a pot over medium-high heat, add the broth, beer and polenta. Simmer, stirring occasionally, until thickened and polenta has softened, about 20 minutes.
Stir in the cream, cheese, and 1 teaspoon salt, allow to cook until absorbed, about 5 minutes.
While the polenta cooks, sauté the chard.
Melt the butter in a pan over medium high heat. Add the chard, cook until softened, about 6 minutes. Stir in the garlic and the salt, remove from heat.
Add the polenta to a serving bowl, top with chard, poached eggs and sprinkle with cheese.
Serve warm.