Combine the soy sauce, honey, and 1 Tbs. water in a small dish and set near the stove. Set a shallow serving dish near the stove, too.
In a 10-inch straight-sided sauté pan, heat the butter with the olive oil over medium-high heat. When the butter is melted, add the green beans and 1/2 tsp. salt and toss with tongs to coat well. Cook, turning the beans occasionally, until most are well browned, shrunken, and tender, 7 to 8 minutes. (The butter in the pan will have turned dark brown.)
Reduce the heat to low, add the garlic, and cook, stirring constantly with a heatproof rubber spatula, until the garlic is softened and fragrant, 15 to 20 seconds. Carefully add the soy mixture (you’ll need to scrape the honey into the pan). Cook, stirring, until the liquid reduces to a glazey consistency that coats the beans, 30 to 45 seconds.
Immediately transfer the beans to the serving dish, scraping the pan with the spatula to get all of the garlicky sauce. Let sit for a few minutes and then serve warm.
Serve these with roast pork or even as a substantial part of a vegetarian meal.