Using a hand mixer, beat goat cheese and heavy cream in a bowl until well combined, about 1 minute. Beat in chives and pepper.
Place the 4 tomato bottoms on a plate and sprinkle with 1/8 tsp of the salt. Spread 2 tbsp of the goat cheese mixture on each tomato bottom. Sprinkle about 2 tsp of the pistachios over each, then drizzle lightly with extra-virgin olive oil and balsamic glaze. Place middle tomato slice on top of each and repeat with remaining
1/8 tsp salt, goat cheese, pistachios, oil and glaze. Place tops on tomatoes.