Heat 1 tbsp. butter in a small frying pan over medium heat, add the shallot, and cook until translucent and starting to brown, about 4 minutes. Remove shallot from pan and add wine. Cook over medium heat until reduced to a thick syrup, about 3 minutes. Remove pan from heat and, using a rubber spatula, scrape syrup into a small bowl. Let cool.
In a food processor, whirl together remaining 1/2 cup butter, cooled shallot, salt, and pepper until blended, about 1 minute. Remove food processor blade and stir in cheese; then drizzle in wine reduction and oregano, stirring just to incorporate (you want the cheese to be in fairly large chunks and the wine to remain in streaks throughout butter).
Lay a piece of plastic wrap on a work surface. Using a rubber spatula, scrape butter lengthwise onto the plastic. Lift the top edge of the plastic up and over the butter to meet the bottom edge of the plastic. Roll butter toward you, evening it out into a log about 4 in. long. Twist ends of the plastic to seal. Chill until firm, about 30 minutes.
Remove plastic wrap and slice off 1/4 in. portions (about 1 tbsp.) to serve over grilled steaks.
Make Ahead: Up to 1 week (keep chilled), or up to 1 month (keep frozen, wrapped in several layers of plastic).
Note: Nutritional analysis is per tbsp.