/u/nhnhnh noted that, in Pythagorean thought, beans were forbidden--that they could even be thought to contain (deceased) "transitioning" human souls. Cf. Pliny, NH 18.118, on this; and for further classic chthonic associations, beans are said to resemble the "gates of Hades" in an Aristotelian fragment (fr. 195 Rose).

The section of Schroeder's Mysterium und Mimus im Rigveda that you mentioned discusses Mars in conjunction with the Roman Lares. (He also cites the Ausführliches Lexikon der griechischen und römischen Mythologie, with the relevant section beginning "Nach Lydus de mens. 4, 29 war die Bohne (κύαμος) dem Mars geheiligt..." = "According to [John the] Lydian, De Mensibus 4, 29, the bean (κύαμος) is sacred to Mars").

Schroeder also mentions the Lemures--who Ovid associates with the Lares. From the Wiki page for the Lares:

If, as Ovid proposes, the lemures are an unsatiated, malevolent and wandering form of Lares, then they and their mother also find their way into Lemuralia, when the hungry Lemures gather in Roman houses and claim cult from the living. The paterfamilias must redeem himself and his family with the offer of midnight libations of spring-water, and black beans spat onto the floor. Any lemures dissatisfied with these offerings are scared away by the loud clashing of bronze pots. Taylor notes the chthonic character of offerings made to fall – or deliberately expelled – towards the earth. If their mother's nature connects the Lares to the earth they are, according to Taylor, spirits of the departed.

McDonough (1997, “Carna, Proca and the Strix on the Kalends of June”) discusses the significance of beans and its connection to some of these things, as well as a festival during the Kalends of June, the Kalendae Fabariae and the goddess Carna:

In Rome, beans were given to ghosts on the Lemuria (discussed below, pp. 25-26), while the Flamen Dialis was forbidden both from eating them (Festus 87M = 77L), and even from uttering their name (Gel. 10.15.12). According to the strictures of philosophers and priests, beans were problematic; among the folk, however, beans were a favorite food, particularly when served with bacon. Even to Horace, whose stomach was notoriously tender (cf. Epod. 3, S. 1.5.7, 49), the mere thought of a simple country dinner consisting of beans and bacon elicited the highest praise (S. 2.6.65): o noctes cenaeque deum! "Oh nights and meals of the gods!"

Further, he writes

we might contrast the customs of the Kalendae Fabariae with the rites of the Lemuria (May ninth, eleventh, and thirteenth), a festival dedicated to bringing inferias tacitis minibus, "offerings to the silent ghosts" (Fast. 5.422).77 The manner in which this was accomplished is clearly described by Ovid: in the middle of the night, the worshiper (thought by most scholars to be the paterfamilias) takes up black beans and, turning his face away, throws them, as he intones haec ego mitto / his...redimo meque meosque fabis, "these I cast, I redeem me and mine with these beans" (Fast. 5.434f.).78 Noting the usage of beans on both the Lemuria and the Kalends of June, and taking further note of their function in other rituals of the dead, Wissowa concluded that the goddess Carna must have been a chthonic goddess. His identification is imprecise, however, since for each day the particular usage of beans is quite different: beans are eaten on June first and, by contrast, are thrown on the Lemuria. The distinction is not insignificant, for the treatment of food on both days is highly significant. The striges and lemurs are supernatural creatures who have come to feast in the household; the food they are given is specifically marked as not being for human consumption and furthermore may no longer even be looked upon by human eyes.

---

As for Indo-European connections beyond the Mediterranean, I'd have to look into it more; but in the Taittiriya Samhita, the ritual for a purusamedha--here, human sacrifice--is described in which 21 beans (māṣas) are brought/thrown with the human head. Oldenberg (1988) asks, with Schroeder, "Was the bean a part of the dead even from the Indo-European period?"

What's PIE? Proto-Indo-European?