In the meantime, grate Parmesan until you have 1 cup grated cheese.
Once water is boiling boiling, slowly pour in the polenta while briskly whisking. Once the polenta starts to stick to the whisk (the whole stirring in, takes maybe 3 minutes) reduce heat to low (!), cover and set an alarm for 10 minutes.
In the meantime, heat a large grilling pan over medium heat.
Wash asparagus and cut about 2 inches of the bottoms off and discard. Then cut asparagus in 2 in the middle.
Wash radishes and cut off tail and leaves. Then cut into 4.
When polenta alarm goes off, add 1 cup grated Parmesan and stir well. Cover again and set alarm for a further 10 minutes.
The grilling pan should be hot by now, add 1 Tbsp butter and once melted add bottom parts of the asparagus only (they take longer to soften). Grill for 2-3 minutes turning occasionally. Then add rest of the vegetables.
Add salt and pepper to vegetables and toss frequently while grilling.
Once polenta alarm goes off, remove pot from heat, add 2 Tbsp butter and stir until melted and incorporated.