Preheat half of your grill to high (or build a bed of moderately hot coals on one half of the grill.
Place the sausage links in a single layer in a heavy-bottomed skillet and pour the beer over the top. Put the lid on the pan and bring up to a boil, covered tightly, over medium high heat. As soon as it boils, remove the lid, drop the heat to low and simmer for 1 minute only.
Transfer the sausages to the hottest part of the grill. Cook them, turning often, until they start to become golden brown.
Immediately move them to the coolest part of the grill and let them cook , turning frequently, until they are very hot all the way through (150°F on an instant read thermometer).
Move the sausages to a platter and tent loosely with foil while working on the peppers and onions.
Heat the olive oil in a heavy-bottomed skillet over medium high heat. Add the sliced peppers, onions, and garlic, sprinkle with salt, and stir to coat. Continue cooking, stirring frequently, until the peppers and onions are tender with just a little bite in the center. Transfer to a bowl.
Serve each sausage on a bun, smeared with yellow mustard and piled with sauteed peppers and onions!